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 with no remainder.

For the numbers 8 and 10, the LCM is 40.

Let’s explore the most efficient way to find it.

Step-by-Step Method To Find LCM

The most effective strategy is to use multiples of the larger number and check if the smaller number divides into any of them.

Example: LCM of 8 and 10

  • $10 \div 8$ → remainder → ❌
  • $10 \times 2 = 20$, $20 \div 8$ → remainder → ❌
  • $10 \times 3 = 30$, $30 \div 8$ → remainder → ❌
  • $10 \times 4 = 40$, $40 \div 8 = 5$ → ✅

So, the LCM of 8 and 10 is 40.

How To Check Your Answer

You can also check your answer by multiplying the two numbers and working backward.

  • $8 \times 10 = 80$

Now count down:

  • $10 \times 7 = 70$, $70 \div 8$ → remainder
  • $10 \times 6 = 60$, $60 \div 8$ → remainder
  • $10 \times 5 = 50$, $50 \div 8$ → remainder
  • $10 \times 4 = 40$, $40 \div 8 = 5$ → ✅
  • $10 \times 3 = 30$, $30 \div 8$ → remainder
  • $10 \times 2 = 20$, $20 \div 8$ → remainder
  • $10 \times 1 = 10$, $10 \div 8$ → remainder

You now have common multiples: (80, 40)
The smallest one is 40, confirming it as the lowest common multiple.

Summary

The lowest common multiple of 8 and 10 is 40.

To find the LCM:

  1. Multiply the larger number by 1, 2, 3… until the smaller number divides in evenly.
  2. You can also confirm by working backward from their product.

Knowing how to find the LCM is especially helpful when adding or subtracting fractions with different denominators.