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# Common Multiples and Least Common Multiple

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Learn how to find common multiples and the least common multiple between two numbers.

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• what is thelcm of 14 4 and 42

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### Common Multiples and Least Common Multiple

1. 1. Common Multiples and Least Common Multiple Mrs. Young EMC 1
2. 2. Product <ul><li>The answer to a multiplication problem. </li></ul>6 X 6 = 36
3. 3. What is the product? 7 X 8 = 56
4. 4. What is the product? 8 X 9 = 72
5. 5. Multiple <ul><li>The product of a whole number multiplied times any other whole number. </li></ul>Some multiples of 6 6, 12, 18, 24, 30, 36, 42
6. 6. Name some multiples of 5 5, 10, 15, 20, 25, 30, 35
7. 7. Name some multiples of 7 7, 14, 21, 28, 35, 42, 49
8. 8. Name some multiples of 4 4, 8, 12, 16, 20, 24, 28
9. 9. Name some multiples of 9 9, 18, 27, 36, 45, 54, 63
10. 10. Common Multiple <ul><li>A number that is a multiple of two or more numbers. </li></ul>
11. 11. Find the least common multiple of 3 and 6 <ul><li>Step 1: List the multiples of both numbers (only list the first 8). </li></ul><ul><li>3: 3, 6, 9, 12, 15, 18, 21, 24 </li></ul><ul><li>6: 6, 12, 18, 24, 30, 36, 42, 48 </li></ul>
12. 12. Step 2: <ul><li>Circle the common multiples </li></ul>3: 3, 6, 9, 12, 15, 18, 21, 24 6: 6, 12, 18, 24, 30, 36, 42, 48
13. 13. Step 3: <ul><li>Find the least common multiple (LCM) </li></ul><ul><li>The least common multiple is the multiple that has the least value but is common between the two numbers. </li></ul>3: 3, 6 , 9, 12 , 15, 18 , 21, 24 6: 6 , 12 , 18 , 24 , 30, 36, 42, 48 So, the least common multiple (LCM) is 6. Note that there is only ONE least common multiple, but there may be more than one common multiple.
14. 14. Find the least common multiple of 9 and 12 Step 1: List the multiples of both numbers (only list the first 8) 9: 9, 18, 27, 36, 45, 54, 63, 72 12: 12, 24, 36, 48, 60, 72, 84, 96
15. 15. Step 2: <ul><li>Circle the common multiples </li></ul>9: 9, 18, 27, 36, 45, 54, 63, 72 12: 12, 24, 36, 48, 60, 72, 84, 96
16. 16. Step 3: <ul><li>Find the least common multiple (LCM) </li></ul><ul><li>The least common multiple is the multiple that has the least value but is common between the two numbers. </li></ul>9: 9, 18, 27, 36 , 45, 54, 63, 72 12: 12, 24, 36 , 48, 60, 72 , 84, 96 So, the least common multiple (LCM) is 36. Note that there is only ONE least common multiple, but there may be more than one common multiple.
17. 17. Find the least common multiple of 4 and 6 <ul><li>Step 1: List the multiples of both numbers (only list the first 8) </li></ul><ul><li>4: 4, 8, 12, 16, 20, 24, 28, 32 </li></ul><ul><li>6: 6, 12, 18, 24, 30, 36, 42, 48 </li></ul>
18. 18. Step 2: <ul><li>Circle the common multiples </li></ul>4: 4, 8, 12, 16, 20, 24, 28, 32 6: 6, 12, 18, 24, 30, 36, 42, 48
19. 19. Step 3: <ul><li>Find the least common multiple (LCM) </li></ul><ul><li>The least common multiple is the multiple that has the least value but is common between the two numbers. </li></ul>4: 4, 8, 12 , 16, 20, 24 , 28, 32 6: 6, 12 , 18, 24 , 30, 36, 42, 48 So, the least common multiple (LCM) is 12. Note that there is only ONE least common multiple, but there may be more than one common multiple.