How do you find the lowest common multiple between two numbers quickly — and how can you check your answer?

The lowest common multiple (LCM) of two numbers is the smallest number that both can divide into with no remainder.

For the numbers 4 and 6, the LCM is 12.

Let’s walk through the most efficient method to find it.

Step-by-Step Method To Find LCM

To find the LCM between two numbers, follow this approach:

  1. Start with the larger number.
  2. Check: can the smaller number divide evenly into it?
  3. If not, multiply the larger number by 2, 3, 4, etc., and check each time until the smaller number divides in cleanly.

Example: Find the LCM of 4 and 6

  • $6 \div 4 = 1$ remainder → ❌
  • $6 \times 2 = 12$, and $12 \div 4 = 3$ → ✅

Therefore, the LCM of 4 and 6 is 12.

How To Check Your Answer

To confirm your answer, you can multiply both numbers together and work backwards to find the lowest valid common multiple.

  • $4 \times 6 = 24$ (a common multiple, not necessarily the lowest)

Now count down:

  • $6 \times 3 = 18$, $18 \div 4 = 4.5$ → ❌
  • $6 \times 2 = 12$, $12 \div 4 = 3$ → ✅
  • $6 \times 1 = 6$, $6 \div 4 = 1.5$ → ❌

Your smallest value that both divide into is 12. That confirms the LCM.

Summary

The lowest common multiple of 4 and 6 is 12.

To find it:

  1. Multiply the larger number by 1, 2, 3… until the smaller number divides in evenly.
  2. Use this method to confidently work with problems involving fractions, where a common denominator is needed.