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
Two lighthouses flash together at 8 pm.

One lighthouse flashes every 36 seconds. The other flashes every 60 seconds.

How many seconds after 8 pm do they next flash together?
Level 4 · 3 marksTry it
2
A florist has 72 roses and 90 tulips.

She makes identical bunches, using every flower.

(a) What is the greatest number of bunches she can make?

(b) How many roses and how many tulips are in each bunch?
Level 4 · 4 marksTry it
3
$A = 2^3 \times 3^2 \times 5$ and $B = 2^2 \times 3^4 \times 7$

(a) Find the highest common factor (HCF) of $A$ and $B$ .

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

Give each answer as a product of prime factors in index form.
Level 4 · 4 marksTry it
4
(a) Write $60$ and $126$ as products of their prime factors.

(b) Find the highest common factor (HCF) of $60$ and $126$ .

(c) Find the lowest common multiple (LCM) of $60$ and $126$ .
Level 4 · 4 marksTry it
5
Hot dog sausages are sold in packs of $10$ . Bread rolls are sold in packs of $8$ .

Dev wants to buy exactly the same number of sausages as rolls.

(a) What is the smallest number of sausages he can buy?

(b) How many packs of each does he buy?
Level 4 · 3 marksTry it