A multiple of a whole number is a product of that number with another whole number. For example, 20 is a multiple of 4 because $20 = 5\boldcdot 4$.

A **common multiple** for two whole numbers is a number that is a multiple of both numbers. For example, 20 is a multiple of 2 and a multiple of 5, so 20 is a common multiple of 2 and 5.

The **least common multiple** (sometimes written as LCM) of two whole numbers is the smallest multiple they have in common. For example, 30 is the least common multiple of 6 and 10.

One way to find the least common multiple of two numbers is to list multiples of each in order until we find the smallest multiple they have in common. Let's find the least common multiple for 4 and 10. First, we list some multiples of each number.

- Multiples of 4: 4, 8, 12, 16,
**20**, 24, 28, 32, 36, **40**, 44...
- Multiples of 10: 10,
**20**, 30, **40**, 50, ...

20 and 40 are both common multiples of 4 and 10 (as are 60, 80, . . . ), but 20 is the smallest number that is on *both* lists, so 20 is the least common multiple.