Drills

Maths drill

HCF & LCM

Find the biggest shared factor and the first shared multiple.

How it works

  • 1Factor = divides exactly. Multiple = appears in a times table. HCF questions look down into the numbers for shared factors; LCM questions count up to a shared multiple.
  • 2HCF means Highest Common Factor: the biggest number that divides exactly into both. LCM means Lowest Common Multiple: the first positive number in both times tables.
  • 3Write HCF or LCM beside the final number. The same pair of numbers can have a small HCF and a much bigger LCM.

Written method desk

Pick the method the question asks for, then copy its working one line at a time.

Level 1 method

HCF using factor pairs

Copy each line

Use it when: Use this when the numbers are small enough to list their factor pairs without too much work.

  1. 1Write every multiplication pair for the first number.
  2. 2Turn the pairs into a factor list, smallest to largest.
  3. 3Do the same for the second number.
  4. 4Underline the factors that appear in both lists.
  5. 5Choose the highest shared factor and label it HCF.

Fully written example

1Find the HCF of 18 and 24
218 pairs: 1×18, 2×9, 3×6
3Factors of 18: 1, 2, 3, 6, 9, 18
424 pairs: 1×24, 2×12, 3×8, 4×6
5Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
6Shared: 1, 2, 3, 6
7HCF = 6
Check it: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. Both divide exactly.
Watch for: Do not choose the last factor you happened to write. Choose the biggest factor in both lists.