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
$A$ 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
2
(a) Write 84 and 120 as products of their prime factors.

(b) Find the highest common factor (HCF) of 84 and 120.

(c) Find the lowest common multiple (LCM) of 84 and 120.
Level 3 · 4 marksTry it
3
Two buses leave the station together at 9:00 am.

Bus A leaves every $20$ minutes. Bus B leaves every $25$ minutes.

At what time will they next leave together?
Level 3 · 3 marksTry it