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

The lowest common multiple (LCM) of two numbers is the smallest number that both divide into evenly.

For the numbers 8 and 12, the LCM is 24.

Let’s look at the most efficient way to find it.

Step-by-Step Method To Find LCM

The most effective method is to use multiples of the larger number and test whether the smaller number divides into them evenly.

Example: LCM of 8 and 12

  • $12 \div 8$ → remainder → ❌
  • $12 \times 2 = 24$, $24 \div 8 = 3$ → ✅

So, the LCM of 8 and 12 is 24.

How To Check Your Answer

Multiply both numbers together to find a common multiple, then work backwards to find the lowest.

  • $8 \times 12 = 96$

Now check smaller multiples of 12:

  • $12 \times 7 = 84$, $84 \div 8$ → remainder
  • $12 \times 6 = 72$, $72 \div 8 = 9$ → ✅
  • $12 \times 5 = 60$, $60 \div 8$ → remainder
  • $12 \times 4 = 48$, $48 \div 8 = 6$ → ✅
  • $12 \times 3 = 36$, $36 \div 8$ → remainder
  • $12 \times 2 = 24$, $24 \div 8 = 3$ → ✅
  • $12 \times 1 = 12$, $12 \div 8$ → remainder

You now have common multiples: (96, 72, 48, 24)
The smallest is 24, confirming the lowest common multiple.

Summary

The lowest common multiple of 8 and 12 is 24.

To find the LCM:

  1. Multiply the larger number by 1, 2, 3… until the smaller number divides into one of the results.
  2. Or, check backwards from the full product.

This method is especially useful for solving fraction problems, where finding a shared denominator is essential.