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 6 and 9, the LCM is 18.

Let’s walk through the most efficient method 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 and testing whether the smaller number divides evenly.

Example: LCM of 6 and 9

  • $9 \div 6$ → remainder → ❌
  • $9 \times 2 = 18$, $18 \div 6 = 3$ → ✅

So, the LCM of 6 and 9 is 18.

How To Check Your Answer

Another approach is to multiply the two numbers and work backwards to find smaller valid common multiples.

  • $6 \times 9 = 54$

Now work downward:

  • $9 \times 5 = 45$, $45 \div 6$ → remainder
  • $9 \times 4 = 36$, $36 \div 6 = 6$ → ✅
  • $9 \times 3 = 27$, $27 \div 6$ → remainder
  • $9 \times 2 = 18$, $18 \div 6 = 3$ → ✅
  • $9 \times 1 = 9$, $9 \div 6$ → remainder

You now have a list of common multiples: (54, 36, 18)
The smallest value is 18, confirming that it is the lowest common multiple.

Summary

The lowest common multiple of 6 and 9 is 18.

To find the LCM:

  1. Multiply the larger number by 1, 2, 3… until the smaller number divides into one of the results.
  2. Use the method of checking backwards from the full product to confirm your result.

Knowing how to find the LCM helps in adding and subtracting fractions and solving arithmetic problems more efficiently.