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 divide into evenly.

For the numbers 6 and 8, the LCM is 24.

Let’s go through the most efficient way to find it.

Step-by-Step Method To Find LCM

The fastest way to find the LCM is by using multiples of the larger number.

Steps:

  1. Start with the larger number.
  2. Ask: can the smaller number divide into it evenly?
  3. If not, multiply the larger number by 2, then 3, and so on.
  4. Stop when the smaller number divides evenly into the current multiple.

Example: LCM of 6 and 8

  • $8 \div 6$ → remainder → ❌
  • $8 \times 2 = 16$, $16 \div 6$ → remainder → ❌
  • $8 \times 3 = 24$, $24 \div 6 = 4$ → ✅

So, the LCM of 6 and 8 is 24.

How To Check Your Answer

Multiply both numbers together to get a common multiple, then work backwards.

  • $6 \times 8 = 48$

Try smaller multiples:

  • $8 \times 5 = 40$, $40 \div 6$ → remainder
  • $8 \times 4 = 32$, $32 \div 6$ → remainder
  • $8 \times 3 = 24$, $24 \div 6 = 4$ → ✅
  • $8 \times 2 = 16$, $16 \div 6$ → remainder
  • $8 \times 1 = 8$, $8 \div 6$ → remainder

You now have two valid common multiples: 48 and 24. The smallest is 24, confirming it is the lowest common multiple.

Summary

The lowest common multiple of 6 and 8 is 24.

To find the LCM quickly:

  1. Start with the larger number.
  2. Multiply it by 1, 2, 3… until the smaller number divides evenly into one of the results.

Knowing how to find the LCM is essential for solving arithmetic problems, especially when adding or subtracting fractions.