CIE IGCSE Maths: Core

Topic Questions

IGCSEMaths: CoreCIETopic QuestionsNumberPrime Factors, HCF & LCM

Syllabus Edition

First teaching 2021

Last exams 2024

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Prime Factors, HCF & LCM

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1
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Write 825 as the product of its prime factors.

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2
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Write 220 as the product of its prime factors.

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3
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Find the lowest common multiple (LCM) of 8 and 14.

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4
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Write 432 as a product of its prime factors.

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5
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Find the highest odd number that is a factor of 60 and a factor of 90.

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6
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Write 54 as a product of its prime factors.

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7
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Work out the lowest common multiple (LCM) of 18 and 21.

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1a
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Write 18 as the product of its prime factors.

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1b
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At a bus stop

  • a red bus arrives every 18 minutes

and

  • a blue bus arrives every 24 minutes.

At 1047 a red bus and a blue bus arrive.

Find the next time when a red bus and a blue bus arrive together.

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2
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Find the highest common factor (HCF) of 126 and 180.

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3
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Gerry and Alain run around a running track.

To run around the track once

  • Gerry always takes 90 seconds
  • Alain always takes 105 seconds.

They start together at the same point.

After how many minutes are they next together at that point?

........................................ min 

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4
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Talan completes one lap of a racetrack every 80 seconds.

i)
Work out how many laps he can complete in one hour.

[2]

ii)
Naima completes one lap of the track every 88 seconds.
Talan and Naima start running from point A on the track at the same time.
They each complete a number of laps of the track.

Work out the smallest number of laps they each complete before they are both at point A again at the same time.

Talan completes ................. laps and Naima completes ................. laps. [3]

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5
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A northbound train leaves Lexford Station every 30 minutes.
A bus leaves Lexford Station every 45 minutes.

At 11 40 a northbound train and a bus leave the station together.

Find the next time when this happens.

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6
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i)
Find the highest common factor (HCF) of 36 and 90.
[2]
ii)
Find the lowest common multiple (LCM) of 36 and 90.
[2]

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7
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i)
Find the highest common factor (HCF) of 28 and 98.

[2]

ii)
Find the lowest common multiple (LCM) of 28 and 98.
[2]

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8
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i)
126 equals 2 cross times 3 squared cross times k
Find the value of k.

k = .......................  [1]

ii)
Write 90 as the product of its prime factors.
[2]
iii)
Find the lowest common multiple (LCM) of 90 and 126.
[2]

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1
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Find the lowest common multiple (LCM) of 48 and 60.

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2
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Write 195 as a product of its prime factors.

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3
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i)
Write 60 as a product of its prime factors.
[2]
ii)
Find the lowest common multiple (LCM) of 36 and 60.
[2]

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4a
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Find the lowest common multiple (LCM) of 15 and 27.

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4b
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Write 432 as the product of its prime factors.

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5
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Find the highest common factor (HCF) of 24 and 108.

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6
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Find the highest common factor (HCF) of 90 and 48.

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7a
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Write 56 as a product of its prime factors.

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7b
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Find the lowest common multiple (LCM) of 56 and 42.

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8
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Find the lowest common multiple (LCM) of 28 and 35.

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9a
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Find the lowest common multiple (LCM) of 12 and 78.

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9b
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Find the highest common factor (HCF) of 12 and 78.

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