Skill: Find common multiples

A common multiple is a number that appears in the multiples of both numbers.

To find common multiples:

1. List some multiples of the first number.
2. List some multiples of the second number.
3. Find the numbers that appear on both lists.

Example: Find the common multiples of $3$ and $4$ that are less than $(40)$.

List multiples of $3$:

$$3,\ 6,\ 9,\ 12,\ 15,\ 18,\ 21,\ 24,\ 27,\ 30,\ 33,\ 36,\ 39$$

List multiples of $4$:

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

Now look for numbers that are on both lists:

$$\boxed{12,\ 24,\ 36}$$

So, the common multiples of $3$ and $4$ that are less than $(40)$ are $(12)$, $(24)$, and $(36)$.

Check one of them: $(24)$ is a multiple of both numbers because

$$3 \times 8=24 \qquad\text{and}\qquad 4 \times 6=24.$$

Remember: common multiples are numbers in the overlapping lists of multiples. Factors are different because they are numbers that divide evenly into another number.