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
Use it when: Use this when the numbers are small enough to list their factor pairs without too much work.
- 1Write every multiplication pair for the first number.
- 2Turn the pairs into a factor list, smallest to largest.
- 3Do the same for the second number.
- 4Underline the factors that appear in both lists.
- 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.