Maths Library

GCF and LCM: Grade 6 math

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.

Open in full editor

What this covers

GCF and LCM is taught in Grade 6 (age 11 to 12) as a topic to introduce. 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 Common Core State Standards. Check wording and codes against the official document.

  • 6.NS.B.4 Find the greatest common factor of two whole numbers and the least common multiple of two numbers.

Sample sheet and answers

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

GCF and LCM

Grade 6 math

Qs
6
Marks
12
NameDateScore / 12
1.
Find the highest common factor (HCF) of 36 and 24.
[2]
2.
Find the lowest common multiple (LCM) of 12 and 16.
[2]
3.
Find the highest common factor (HCF) of 25 and 20.
[2]
4.
Find the highest common factor (HCF) of 8 and 12.
[2]
5.
Find the highest common factor (HCF) of 10 and 6.
[2]
6.
Find the lowest common multiple (LCM) of 15 and 30.
[2]

Answer key

  1. 12List the factors of each and pick the largest shared one; HCF = 12
  2. 48Use LCM = 12 × 16 ÷ HCF = 192 ÷ 4; LCM = 48
  3. 5List the factors of each and pick the largest shared one; HCF = 5
  4. 4List the factors of each and pick the largest shared one; HCF = 4
  5. 2List the factors of each and pick the largest shared one; HCF = 2
  6. 30Use LCM = 15 × 30 ÷ HCF = 450 ÷ 15; LCM = 30