LCM stands for Least Common Multiple. If you’re wondering how to find the LCM, it’s the smallest number that two or more numbers can divide into evenly—without leaving a remainder. In this post, we’ll explain how to find the Least Common Multiple step by step.

Methods to Find the LCM

There are two common methods to determine the LCM. Choose the one that works best for your numbers:

Method 1: List the Multiples

1. Write a few multiples of each number
2. Find the smallest number that appears in all the lists.
3. That number is the LCM

Examples

Example 1: Find LCM of 4 and 5

• Multiples of 4: 4, 8, 12, 16, 20, 24,….
• Multiples of 5: 5, 10, 15, 20, 25,…..
  ⇒LCM = 20

Example 2: Find LCM of 6, 8 and 12

• Multiples of 6: 6, 12, 18, 24, 30,….
• Multiples of 8: 8, 16, 24, 32,….
• Multiples of 12 : 12,24,36,48,….
  ⇒ LCM = 24

Method 2: Use Prime Factorization

1. Break each number down into its prime factors.
2. Take the highest powers of all the prime numbers involved.
3. Multiply those together to get the LCM.

Examples

Example 1: Find LCM of 12, 15, and 20

• 12 = 2² × 3
• 15 = 3 × 5
• 20 = 2² × 5

Now take the highest powers of all the prime numbers and multiply them:

⇒ LCM = 2² × 3 × 5 = 60
⇒ LCM = 60

Example 2: find the LCM of 4, 6, 12, and 18

• 4 = 2 × 2 = 2²
• 6 = 2 × 3 = 2 × 3
• 12 = 2 × 2 × 3 = 2² × 3
• 18 = 2 × 3 × 3 = 2 × 3²

Now take the highest powers of all the prime numbers and multiply them:

⇒LCM = 2² × 3²
⇒LCM= 4 × 9
⇒LCM= 36

Final Tip

• Use “List the Multipliers” for small, simple numbers
• Use “Prime factorization” for bigger or multiple numbers