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Common Multiples

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Common Multiples:

1) What are the multiples 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, 36,...
We observe that 12, 24, 36,... are multiples of both 4 and 6. They are called the common multiples of 4 and 6.

2) Find the common multiples of 3, 5, and 6.

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36,...
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35,...
Multiples of 6 are 6, 12, 18, 24, 30,...
Common multiples of 3, 5, and 6 are 30, 60,...

Example

Find the first three common multiples of 12 and 18.

12 and 18

Multiples of 12 = 12, 24, 36, 48

Multiples of 18 = 18, 36, 54, 72

3 common multiples = 36, 72, 108.

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