NUMBER

Lowest Common Multiple

Learn the reliable method for lowest common multiple, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Common multiples appear in the times tables of two or more numbers; the LCM is the smallest positive one.

Picture itBuild the times-table sequence
2 · THE METHOD

Follow these steps

  1. List multiples of each number in increasing order.
  2. Mark the values shared by every list.
  3. For the LCM, choose the first positive shared multiple.
3 · WORKED EXAMPLES

See the method in action

Example 1

What is the lowest common multiple of 6 and 9?

  1. The lowest shared multiple of 6 and 9 is 18: 6 × 3 = 9 × 2 = 18.
  2. This is the smallest positive number divisible by both.
Answer: 18
Example 2

Two lights flash together. One flashes every 30 seconds and the other every 45 seconds. How many seconds pass before they next flash together?

  1. The lowest shared multiple of 30 and 45 is 90: 30 × 3 = 45 × 2 = 90.
  2. This is the first positive time satisfying both intervals.
Answer: 90
4 · ELEVENSPRINT TIP

A useful shortcut

For the LCM, choose the first positive shared multiple.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.