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 2 are 2, 4, 6, 8, 10 The multiples of 3 are:

The multiples of 3 are 3, 6, 9, 12, 15 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.

Finding the Least Common Multiple of More than Two Numbers

In the examples here, the least common multiple has been been found for two numbers. But the same procedure extends to any number of numbers.