Find common multiples

A common multiple is a whole number that appears in the multiples of each of two or more given whole numbers, or equivalently is divisible by each of them. Learners can generate and compare multiples using multiplication facts, skip-counting sequences, or number lines, and verify that a number belongs to all relevant sequences; the focus is on concrete whole-number cases rather than prime-factorization methods or abstract generalizations.

Detailed Explanation: Find common multiples

A common multiple is a number that appears in the multiples of two or more numbers.

To find common multiples:

List the multiples of each number.
Look for numbers that appear in both lists.
Check by dividing or multiplying to make sure the number works for both.

Example: Find the first three common multiples of $4$ and $6$ .

List multiples of $4$ :

4,\ 8,\ 12,\ 16,\ 20,\ 24,\ 28,\ 32,\ 36

List multiples of $6$ :

6,\ 12,\ 18,\ 24,\ 30,\ 36

Now compare the lists. The numbers that appear in both are:

12,\ 24,\ 36

So, the first three common multiples of $4$ and $6$ are:

\boxed{12,\ 24,\ 36}

Check one of them:

$(12 = 4 \times 3)$
$(12 = 6 \times 2)$

Because $(12)$ is a multiple of both $4$ and $6$ , it is a common multiple.

Learn by doing: Find common multiples

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Finding Lowest Common Multiple

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Find common multiples

Detailed Explanation: Find common multiples

Learn by doing: Find common multiples

Practice with unlimited practice problems

Practice:

Finding Lowest Common Multiple