How to Find the Least Common Multiple

The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. It is used often when finding common denominators for fractions. This guide shows two ways to find it.

Method 1: List the multiples

Write out the multiples of each number in order and find the first one they share.

Let's try 6 and 8. The multiples of 6 are 6, 12, 18, 24, 30, and so on. The multiples of 8 are 8, 16, 24, 32, and so on. The first shared value is 24, so the least common multiple is 24.

Method 2: Use prime factorization

For larger numbers, prime factorization is quick. Break each number into a product of primes, then collect every prime that appears, each at its highest power.

6 = 2 × 3 and 8 = 2^3. The primes are 2 and 3. Take 2 at the higher power (2^3) and 3 at the higher power (3^1). Multiplying gives 2^3 × 3 = 24, the same answer as listing multiples.

Common mistakes

A frequent mistake is confusing the LCM with the GCD. The LCM is a shared multiple, so it is no smaller than the original numbers. If your answer comes out smaller than the numbers, something went wrong.

With prime factorization, another slip is taking primes at their lowest power. For the LCM, you take the highest power of each prime.

What is it used for?

The least common multiple is used to find common denominators when adding or subtracting fractions. The fraction calculator shows the common-denominator steps, and the GCD and LCM calculator lets you check your answer.