LCM Calculator

The least common multiple (LCM) of two or more integers is the smallest number that is a multiple of all of them.

How to Find the LCM

There are several ways to find the least common multiple.

1. Listing Multiples

   Write down multiples of both numbers until the common one is found.

   Let's find the LCM of 9 and 12.

   • Multiples of 9: 9, 18, 27, 36 ...
   • Multiples of 12: 12, 24, 36, 36 ...
   • LCM = 36

   Obviously, this way is not convenient for big numbers.

2. Prime Factorization

   This method is super reliable and works well especially with big numbers.

   Steps:

   • Break down each number into its prime factors.
   • Look at all the unique prime numbers involved, and for each prime, use the highest exponent (power) from any number.
   • Multiply the highest powers together.

   LCM (9, 12)

   • 9 = 3 × 3 = 3²
   • 12 = 2 × 2 × 3 = 2² × 3
   • Factors with the highest powers: 3² and 2²
   • 3² × 2² = 36

   Use our calculator to get detailed solution using prime factorization method.

3. Using the GCD

   This method is great if the GCD is already known. But it is applicable only for two numbers.

   In order to calculate LCM using GCD, multiply the numbers and divide the product by GCD.

   Formula:

   LCM(a, b) = |a × b|GCD(a, b)

   Find the LCM of 8 and 12.

   • GCD(8, 12) = 4
   • LCM = (8 × 12) ÷ 4 = 96 ÷ 4 = 24