The document discusses the least common multiple (LCM) of numbers. The LCM of two or more numbers is the smallest positive number that is a multiple of each number. Two methods are presented for finding the LCM: 1) listing the multiples of each number and finding their common multiples, and 2) factorizing each number and taking the highest power of each prime factor. Examples are provided to illustrate both methods. The least common denominator (LCD) of fractions is also introduced as being the LCM of the denominators.

1. LCM and LCD

2. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers.

3. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.

4. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, …

5. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,…

6. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12,

7. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12.

8. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12. We may improve the above listing-method for finding the LCM.

9. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12. We may improve the above listing-method for finding the LCM. Given two or more numbers, we start with the largest number,

10. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12. We may improve the above listing-method for finding the LCM. Given two or more numbers, we start with the largest number, list its multiples in order until we find the one that can divide all the other numbers.

11. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12. We may improve the above listing-method for finding the LCM. Given two or more numbers, we start with the largest number, list its multiples in order until we find the one that can divide all the other numbers.Example B. Find the LCM of 8, 9, and 12.

12. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12. We may improve the above listing-method for finding the LCM. Given two or more numbers, we start with the largest number, list its multiples in order until we find the one that can divide all the other numbers.Example B. Find the LCM of 8, 9, and 12. The largest number is 12 and the multiples of 12 are 12, 24, 36, 48, 60, 72, 84 …

13. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12. We may improve the above listing-method for finding the LCM. Given two or more numbers, we start with the largest number, list its multiples in order until we find the one that can divide all the other numbers.Example B. Find the LCM of 8, 9, and 12. The largest number is 12 and the multiples of 12 are 12, 24, 36, 48, 60, 72, 84 … The first number that is also a multiple of 8 and 9 is 72.

14. LCM and LCDDefinition of LCMThe least common multiple (LCM) of two or more numbers is the least number that is the multiple of all of these numbers. Example A. Find the LCM of 4 and 6.The multiples of 4 are 4, 8, 12, 16, 20, 24, … The multiples of 6 are 6, 12, 18, 24, 30,… The smallest of the common multiples is 12, then LCM{4, 6 } = 12. We may improve the above listing-method for finding the LCM. Given two or more numbers, we start with the largest number, list its multiples in order until we find the one that can divide all the other numbers.Example B. Find the LCM of 8, 9, and 12. The largest number is 12 and the multiples of 12 are 12, 24, 36, 48, 60, 72, 84 … The first number that is also a multiple of 8 and 9 is 72. Hence LCM{8, 9, 12} = 72.

15. LCM and LCDBut when the LCM is large, the listing method is cumbersome.

16. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead.

17. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM:

18. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely

19. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations.

20. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.

21. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.

22. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely,

23. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 23

24. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 5

25. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 * 32

26. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 * 32From the factorization select the highest degree of each prime factor:

27. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 * 32From the factorization select the highest degree of each prime factor:

28. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 *32From the factorization select the highest degree of each prime factor

29. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 *518 = 2 *32From the factorization select the highest degree of each prime factor: 23, 32, 5,

30. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 * 32From the factorization select the highest degree of each prime factor: 23, 32, 5, then LCM{8, 15, 18} = 23*32*5 = 8*9*5 = 360.

31. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 * 32From the factorization select the highest degree of each prime factor: 23, 32, 5, then LCM{8, 15, 18} = 23*32*5 = 8*9*5 = 360.

32. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 * 32From the factorization select the highest degree of each prime factor: 23, 32, 5, then LCM{8, 15, 18} = 23*32*5 = 8*9*5 = 360. The LCM of the denominators of a list of fractions is called the least common denominator (LCD).

33. LCM and LCDBut when the LCM is large, the listing method is cumbersome. It's easier to find the LCM by constructing it instead. To construct the LCM: a. Factor each number completely b. For each prime factor, take the highest power appearing in the factorizations. The LCM is their product.Example C. Construct the LCM of {8, 15, 18}.Factor each number completely, 8 = 2315 = 3 * 518 = 2 * 32From the factorization select the highest degree of each prime factor: 23, 32, 5, then LCM{8, 15, 18} = 23*32*5 = 8*9*5 = 360. The LCM of the denominators of a list of fractions is called the least common denominator (LCD). Following is anapplication of the LCM.

34. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6.

35. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. In picture:MaryJoeChuck

36. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? In picture:MaryJoeChuck

37. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuck

38. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching.

39. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, …

40. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM.

41. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices

42. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 1Joe gets 12*3

43. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 1Joe gets 12* = 4 slices3

44. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 11Mary gets 12*Joe gets 12* = 4 slices43

45. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 11Mary gets 12* = 3 slicesJoe gets 12* = 4 slices43

46. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 11Mary gets 12* = 3 slicesJoe gets 12* = 4 slices431Chuck gets 12*6

47. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 11Mary gets 12* = 3 slicesJoe gets 12* = 4 slices431Chuck gets 12* = 2 slices6

48. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 11Mary gets 12* = 3 slicesJoe gets 12* = 4 slices431Chuck gets 12* = 2 slices6In total, that is 4 + 2 + 3 = 9 slices,

49. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 11Mary gets 12* = 3 slicesJoe gets 12* = 4 slices431Chuck gets 12* = 2 slices69In total, that is 4 + 2 + 3 = 9 slices, or of the pizza.12

50. LCM and LCDExample D. From one pizza, Joe wants 1/3, Mary wants 1/4 and Chuck wants 1/6. How many equal slices should we cut the pizza into and how many slices should each person take? What is the fractional amount of the pizza they want in total? In picture:MaryJoeChuckWe find the LCM of 1/3, 1/4, 1/6 by searching. The multiples of 6 are 6, 12, 18, 24, … Since 12 is also the multiple of 3 and 4, then 12 is the LCM. Hence we should cut it into 12 slices and 11Mary gets 12* = 3 slicesJoe gets 12* = 4 slices431Chuck gets 12* = 2 slices693In total, that is 4 + 2 + 3 = 9 slices, or of the pizza.=124

51. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take?

52. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312

53. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator.

54. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:

55. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:To convert the fraction into a fraction with denominator d, the new numerator is * d. abab

56. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:To convert the fraction into a fraction with denominator d, the new numerator is * d. abab9Example D: Convert to a fraction with denominator 48.16

57. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:To convert the fraction into a fraction with denominator d, the new numerator is * d. abab9Example D: Convert to a fraction with denominator 48. The new denominator is 48, 16

58. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:To convert the fraction into a fraction with denominator d, the new numerator is * d. abab9Example D: Convert to a fraction with denominator 48. The new denominator is 48, then the new numerator is 48* 16916

59. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:To convert the fraction into a fraction with denominator d, the new numerator is * d. abab9Example D: Convert to a fraction with denominator 48. The new denominator is 48, then the new numerator is 48* 169316

60. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:To convert the fraction into a fraction with denominator d, the new numerator is * d. abab9Example D: Convert to a fraction with denominator 48. The new denominator is 48, then the new numerator is 48* = 27. 169316

61. LCM and LCDYour Turn: From one pizza, Joe wants 3/8 of it, Mary wants 1/6 of it and Chuck wants 5/12 of it. How many equal slices should we cut the pizza and how many slices should each person take? 14In the above example, we found that is the same .312The following theorem tells us how to convert the denominator of a fraction to a fraction with a different denominator. Multiplier Theorem:To convert the fraction into a fraction with denominator d, the new numerator is * d. abab9Example D: Convert to a fraction with denominator 48. The new denominator is 48, then the new numerator is 48* = 27. 1693927Hence = 1648 .16

62. LCM and LCDExercise A. Find the LCM.1. a.{6, 8} b. {6, 9} c. {3, 4} d. {4, 10} 2. a.{5, 6, 8} b. {4, 6, 9} c. {3, 4, 5} d. {4, 6, 10} a.{6, 8, 9} b. {6, 9, 10} c. {4, 9, 10} d. {6, 8, 10} 4. a.{4, 8, 15} b. {8, 9, 12} c. {6, 9, 15} 5. a.{6, 8, 15} b. {8, 9, 15} c. {6, 9, 16} 6. a.{8, 12, 15} b. { 9, 12, 15} c. { 9, 12, 16} 7. a.{8, 12, 18} b. {8, 12, 20} c. { 12, 15, 16} 8. a.{8, 12, 15, 18} b. {8, 12, 16, 20} 9. a.{8, 15, 18, 20} b. {9, 16, 20, 24}

63. LCM and LCDB. Convert the fractions to fractions with the given denominators.10. Convert to denominator 12.11. Convert to denominator 24.12. Convert to denominator 36.13. Convert to denominator 60.23573 ,4 ,6 ,4 13536 ,4 ,6 ,8 7581112 ,4 ,9 ,6 97131110 ,12 ,5 ,15