GCSE · Integers, powers & roots

HCF and LCMExam-style questions

What highest common factor and lowest common multiple actually mean, how prime factors give both (lowest powers vs highest powers), and how to spot which one a word problem is asking for.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Find the highest common factor (HCF) of $12$ and $18$ .
Level 1 · 2 marksTry it
2
Find the lowest common multiple (LCM) of $6$ and $8$ .
Level 1 · 2 marksTry it
3
(a) Find the highest common factor (HCF) of $24$ and $36$ (1 mark)

(b) Find the lowest common multiple (LCM) of $24$ and $36$ (1 mark)
Level 2 · 2 marksTry it
4
(a) Find the highest common factor (HCF) of $12$ and $18$ .

(b) Find the lowest common multiple (LCM) of $12$ and $18$ .
Level 2 · 2 marksTry it
5
$A$ and $B$ are numbers such that

$A = 2^3 \times 5^2 \times 11$

$B = 5 \times 11^2$
(a) Find the highest common factor (HCF) of $A$ and $B$ .

(1 mark)
(b) Find the lowest common multiple (LCM) of $A$ and $B$ .

(2 marks)
Level 3 · 3 marksTry it

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