## The Lesson

The least common multiple is the smallest multiple that is common to two or more numbers.## Understanding the Least Common Multiple

The multiples of a number are the numbers that result when that number is multiplied by an integer (a whole number). The multiples of**2**are found by multiplying 2 by successive integers: 2 × 1 = 2 , 2 × 2 = 4...

The multiples of

**3**are:

We see that 6 and 12 are both multiples of 2

**and**3. They are

**common multiples**. 6 is the smallest of the common multiples. It is the

**least common multiple**of 2 and 3.

## How to Find the Least Common Multiple

The least common multiple of any numbers can be found. If you wanted to find the least common multiple of**3**and

**4**, you would first list the multiples of each number...

Multiples of 3 = 3, 6, 9, 12, 15, 18
Multiples of 4 = 4, 8, 12, 16, 20, 24

...then find the smallest factor that appears in both lists:
Multiples of 3 = 3, 6, 9,

**12**, 15, 18 Multiples of 4 = 4, 8,**12**, 16, 20, 24**12**is the least common multiple because it is the smallest multiple of both 3 and 4.

Read more about how to find the least common multiple

## What's in a Name?

The least common multiple (LCM) is so called because it is the smallest (*least*)

*multiple*that is the same (

*common*) to the numbers.

## What Is a Multiple?

A multiple is the result of multiplying a number by an integer (a whole number). For example, the multiples of 3 are:
3, 6, 9, 12, 15

- 3 is the result of multiplying 3 by 1.
- 6 is the result of multiplying 3 by 2.
- 9 is the result of multiplying 3 by 3.
- 12 is the result of multiplying 3 by 4.
- 15 is the result of multiplying 3 by 5.