Maths Library

Highest Common Factor and Lowest Common Multiple: Year 8 maths

Pupils find the highest common factor and lowest common multiple of two or three numbers. Worksheets progress from listing factors and multiples to using prime factorisation and Venn diagrams.

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What this covers

Highest Common Factor and Lowest Common Multiple is taught in Year 8 (age 12 to 13, KS3) as a main teaching focus. It sits in the Number strand.

Worked example

Find the HCF and LCM of 24 and 36.

  1. Prime factorisation: 24 = 2^3 × 3, 36 = 2^2 × 3^2
  2. HCF takes lowest powers: 2^2 × 3 = 12
  3. LCM takes highest powers: 2^3 × 3^2 = 72

Answer: HCF = 12, LCM = 72

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Find HCF or LCM of two single-digit numbers by simple listing
  2. Find HCF and LCM of two two-digit numbers up to 30
  3. Find HCF and LCM of two numbers up to 100 using prime factor trees
  4. Find HCF and LCM of three two-digit numbers using prime factorisation
  5. Solve context word problems requiring identification and calculation of HCF or LCM

Common mistakes

  • Confusing factors with multiples, giving an LCM smaller than the original numbers
  • Multiplying the two numbers together instead of finding the lowest common multiple

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Find highest common factors, lowest common multiples, and prime factorisations of integers.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Highest Common Factor and Lowest Common Multiple

Year 8 maths

Qs
6
Marks
24
NameDateScore / 24
1.
Find the highest common factor (HCF) of 66 and 44.
[4]
2.
Find the lowest common multiple (LCM) of 21 and 28.
[4]
3.
Find the highest common factor (HCF) of 50 and 40.
[4]
4.
Find the highest common factor (HCF) of 14 and 21.
[4]
5.
Find the highest common factor (HCF) of 20 and 12.
[4]
6.
Find the lowest common multiple (LCM) of 27 and 54.
[4]

Answer key

  1. 22List the factors of each and pick the largest shared one; HCF = 22
  2. 84Use LCM = 21 × 28 ÷ HCF = 588 ÷ 7; LCM = 84
  3. 10List the factors of each and pick the largest shared one; HCF = 10
  4. 7List the factors of each and pick the largest shared one; HCF = 7
  5. 4List the factors of each and pick the largest shared one; HCF = 4
  6. 54Use LCM = 27 × 54 ÷ HCF = 1458 ÷ 27; LCM = 54