Common Multiples and Common Multiples and Least Common MultipleLeast Common Multiple

Mrs. Young

EMC 1

ProductProduct

The answer to a The answer to a multiplication problem.multiplication problem.

6 X 6 = 36

What is the product?What is the product?

7 X 8 = 56

What is the product?What is the product?

8 X 9 = 72

MultipleMultiple

The product of a whole number The product of a whole number multiplied times any other whole multiplied times any other whole number.number.

Some multiples of 6 6, 12, 18, 24, 30, 36, 42

Name some multiples Name some multiples of 5of 5

5, 10, 15, 20, 25, 30, 35

Name some multiples Name some multiples of 7of 7

7, 14, 21, 28, 35, 42, 49

Name some multiples Name some multiples of 4of 4

4, 8, 12, 16, 20, 24, 28

Name some multiples Name some multiples of 9of 9

9, 18, 27, 36, 45, 54, 63

Common MultipleCommon Multiple

A number that is a multiple A number that is a multiple of two or more numbers.of two or more numbers.

Find the least common Find the least common multiple of 3 and 6multiple of 3 and 6

Step 1: List the multiples of Step 1: List the multiples of both numbers (only list the both numbers (only list the first 8).first 8).

3: 3, 6, 9, 12, 15, 18, 21, 243: 3, 6, 9, 12, 15, 18, 21, 24

6: 6, 12, 18, 24, 30, 36, 42, 486: 6, 12, 18, 24, 30, 36, 42, 48

Step 2:Step 2:

Circle the common multiplesCircle the common multiples

3: 3, 6, 9, 12, 15, 18, 21, 3: 3, 6, 9, 12, 15, 18, 21, 2424

6: 6, 12, 18, 24, 30, 36, 42, 6: 6, 12, 18, 24, 30, 36, 42, 4848

Step 3:Step 3:Find the least common multiple (LCM)Find the least common multiple (LCM)

The least common multiple is the multiple that has the The least common multiple is the multiple that has the least value but is common between the two numbers.least value but is common between the two numbers.

3: 3, 3: 3, 66, 9, , 9, 1212, 15, , 15, 1818, 21, , 21, 2424

6: 6: 66, , 1212, , 1818, , 2424, 30, 36, 42, 48, 30, 36, 42, 48So, 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.

Find the least common Find the least common multiple of 9 and 12multiple 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

Step 2:Step 2:

Circle the common multiplesCircle the common multiples

9: 9, 18, 27, 36, 45, 54, 63, 72

12: 12, 24, 36, 48, 60, 72, 84, 96

Step 3:Step 3: Find the least common multiple (LCM)Find the least common multiple (LCM)

The least common multiple is the multiple that has the The least common multiple is the multiple that has the least value but is common between the two numbers.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, 96So, 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.

Find the least common Find the least common multiple of 4 and 6multiple of 4 and 6

Step 1: List the multiples of Step 1: List the multiples of both numbers (only list the both numbers (only list the first 8)first 8)

4: 4, 8, 12, 16, 20, 24, 28, 324: 4, 8, 12, 16, 20, 24, 28, 32

6: 6, 12, 18, 24, 30, 36, 42, 486: 6, 12, 18, 24, 30, 36, 42, 48

Step 2:Step 2:Circle the common multiplesCircle the common multiples

4: 4, 8, 12, 16, 20, 24, 28, 324: 4, 8, 12, 16, 20, 24, 28, 32

6: 6, 12, 18, 24, 30, 36, 42, 486: 6, 12, 18, 24, 30, 36, 42, 48

Step 3:Step 3:Find the least common multiple (LCM)Find the least common multiple (LCM)

The least common multiple is the multiple that has the The least common multiple is the multiple that has the least value but is common between the two numbers.least value but is common between the two numbers.

4: 4, 8, 4: 4, 8, 1212, 16, 20, , 16, 20, 2424, 28, 32, 28, 32

6: 6, 6: 6, 1212, 18, , 18, 2424, 30, 36, 42, 48, 30, 36, 42, 48So, 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.