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 3 and 5, the LCM is 15.

Let’s explore the most efficient method to arrive at that answer.

Step-by-Step Method To Find LCM

To find the LCM between two numbers, follow these steps:

  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.

This is the most efficient method.

Example: Find the LCM of 3 and 5

  • $5 \div 3 = 1$ remainder → ❌
  • $5 \times 2 = 10$, and $10 \div 3 = 3$ remainder → ❌
  • $5 \times 3 = 15$, and $15 \div 3 = 5$ → ✅

Therefore, the LCM of 3 and 5 is 15.

How To Check Your Answer

A quick way to check is to multiply both numbers together and then work backwards to confirm that no smaller value is valid.

  • $3 \times 5 = 15$

Try smaller multiples of 5:

  • $5 \times 2 = 10$, $10 \div 3 = 3.33$ → ❌
  • $5 \times 1 = 5$, $5 \div 3 = 1.66$ → ❌

Only $15$ is divisible by both 3 and 5, confirming it is the lowest common multiple.

Summary

The lowest common multiple of 3 and 5 is 15.

To find it quickly:

  1. Start with the larger number.
  2. Multiply it by 1, 2, 3… and check if the smaller number divides evenly.
  3. The first match is your LCM.

This strategy is especially useful when working with fractions, where finding a common denominator is required.