# Least Common Multiple

## What Is the Least Common Multiple?

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.