The document explains the concepts of products, multiples, common multiples, and least common multiples (LCM). It provides a step-by-step guide on how to find the LCM of different pairs of numbers, illustrating the process with examples. The key takeaway is that the LCM is the smallest number that is a multiple of the two given numbers and there can be multiple common multiples.

1. Common Multiples and
Least Common Multiple
Mr.PREM
CHAPTER 1.3

2. Product
 The answer to a
multiplication problem.
6 X 6 = 36

3. What is the product?
7 X 8 = 56

4. What is the product?
8 X 9 = 72

5. Multiple
 The product of a whole number
multiplied times any other whole
number.
Some multiples of 6
6, 12, 18, 24, 30, 36, 42

6. Name some multiples
of 5
5, 10, 15, 20, 25,
30, 35

7. Name some multiples
of 7
7, 14, 21, 28, 35,
42, 49

8. Name some multiples
of 4
4, 8, 12, 16, 20,
24, 28

9. Name some multiples
of 9
9, 18, 27, 36, 45, 54, 63

10. Common Multiple
 A COMMON number that is
a multiple of two or more
numbers.

11. LOWEST COMMON
MULTIPLE
 The smallest common multiple
obtained and it is the first common
multiple if listed.

12. Find the least common
multiple of 3 and 6
Step 1: List the multiples of
both numbers (only list the
first 8).
3: 3, 6, 9, 12, 15, 18, 21, 24
6: 6, 12, 18, 24, 30, 36, 42, 48

13. Step 2:
Circle the common multiples
3: 3, 6, 9, 12, 15, 18, 21, 24
6: 6, 12, 18, 24, 30, 36, 42, 48

14. Step 3:
Find the least common multiple
(LCM)
 The least common multiple is the
multiple that has the least value but is
common between the two numbers.
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.

15. 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

16. Step 2:
Circle the common multiples
9: 9, 18, 27, 36, 45, 54, 63, 72
12: 12, 24, 36, 48, 60, 72, 84, 96

17. Step 3:
Find the least common multiple
(LCM)
 The least common multiple is the
multiple that has the least value but is
common between the two numbers.
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.

18. Find the least common
multiple of 4 and 6
 Step 1: List the multiples of
both numbers (only list the
first 8)
4: 4, 8, 12, 16, 20, 24, 28, 32
6: 6, 12, 18, 24, 30, 36, 42, 48

19. Step 2:
Circle the common multiples
4: 4, 8, 12, 16, 20, 24, 28, 32
6: 6, 12, 18, 24, 30, 36, 42, 48

20. Step 3:
Find the least common multiple
(LCM)
 The least common multiple is the
multiple that has the least value but is
common between the two numbers.
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.