IGCSEMaths: ExtendedCIEExam QuestionsNumberPrime Factors, HCF & LCM

Syllabus Edition

First teaching 2023

First exams 2025

|

Prime Factors, HCF & LCM (CIE IGCSE Maths: Extended)

Exam Questions

2 hours41 questions

Select a question set to download for
Prime Factors, HCF & LCM

Select an answer set to view for
Prime Factors, HCF & LCM

Easy
Medium
Hard
1
Sme Calculator2 marks

Write 84 as a product of its prime factors.

How did you do?

Did this page help you?

2
Sme Calculator3 marks

Write 525 as a product of its prime factors.

How did you do?

Did this page help you?

3
Sme Calculator3 marks

Trams leave Piccadilly

to Eccles every 9 minutes
to Didsbury every 12 minutes

A tram to Eccles and a tram to Didsbury both leave Piccadilly at 9 am.

At what time will a tram to Eccles and a tram to Didsbury next leave Piccadilly at the same time?

How did you do?

Did this page help you?

1
Sme Calculator2 marks

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

How did you do?

Did this page help you?

2a
Sme Calculator2 marks

Write 56 as a product of its prime factors.

How did you do?

2b
Sme Calculator2 marks

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

How did you do?

Did this page help you?

3
Sme Calculator3 marks

Buses to Acton leave a bus station every 24 minutes.
Buses to Barton leave the same bus station every 20 minutes.

A bus to Acton and a bus to Barton both leave the bus station at 9 00 am.

When will a bus to Acton and a bus to Barton next leave the bus station at the same time?

How did you do?

Did this page help you?

4a
Sme Calculator3 marks

Express 180 as a product of its prime factors.

How did you do?

4b
Sme Calculator2 marks

Martin thinks of two numbers.

He says,

"The Highest Common Factor (HCF) of my two numbers is 6
The Lowest Common Multiple (LCM) of my two numbers is a multiple of 15"

Write down two possible numbers that Martin is thinking of.

How did you do?

Did this page help you?

5a
Sme Calculator2 marks

A equals space 3 squared space cross times space 5 to the power of 4 space cross times space 7 space space space space space space space space space space space space space space space space space space space space space B space equals space 3 to the power of 4 space cross times space 5 cubed space cross times space 7 space cross times space 11

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

How did you do?

5b
Sme Calculator2 marks

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

How did you do?

Did this page help you?

6
Sme Calculator2 marks

A space equals space 3 to the power of 5 cross times space 5 space cross times space 7 to the power of 3 space end exponent B space equals space 2 cubed cross times space 3 space cross times space 7 to the power of 4

i)
Find the Highest Common Factor (HCF) of A and B.

[1]

ii)
Find the Lowest Common Multiple (LCM) of space A spaceand B.
[1]

How did you do?

Did this page help you?

7
Sme Calculator2 marks

Work out the lowest common multiple (LCM) of 36 and 120.

How did you do?

Did this page help you?

8
Sme Calculator2 marks

table row blank blank cell A space equals space 2 cubed cross times 3 squared cross times 5 squared cross times 11 B space equals space 2 to the power of 4 cross times 3 cross times 5 to the power of 4 cross times 13 end cell end table

Find the lowest common multiple (LCM) of space A spaceand B.
Give your answer as a product of powers of prime numbers.

How did you do?

Did this page help you?

9
Sme Calculator3 marks

A machine has a buzzer that sounds every 50 minutes.
The machine also has a bell that sounds every 80 minutes.

The buzzer and the bell sound together at 10 am.

Find the time at which they next sound together.

How did you do?

Did this page help you?

10
Sme Calculator2 marks

Work out the lowest common multiple (LCM) of 120 and 144.

How did you do?

Did this page help you?

11a
Sme Calculator2 marks

Written as the product of its prime factors

672 space equals space 2 to the power of 5 space end exponent cross times space 3 space cross times space 7

Write 252 as the product of its prime factors.

How did you do?

11b
Sme Calculator1 mark

Work out the value of the highest common factor of 672 and 252.

How did you do?

Did this page help you?

1
Sme Calculator1 mark

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

How did you do?

Did this page help you?

2
Sme Calculator3 marks

Here are three lamps.

q4-1-3-hard-ocr-gcse-maths-extended

Lamp A flashes every 20 seconds.
Lamp B flashes every 45 seconds.
Lamp C flashes every 120 seconds.

The three lamps start flashing at the same time.

How many times in one hour will the three lamps flash at the same time?

How did you do?

Did this page help you?

3a
Sme Calculator2 marks

Find the lowest common multiple (LCM) of 40 and 56.

How did you do?

3b
Sme Calculator1 mark

A space equals space 2 cubed space cross times space 3 space cross times space 5 space space space space space space space space space space space space space space space space space space space space space space B space equals space 2 to the power of 2 space end exponent cross times space 3 space cross times space 5 squared

Write down the highest common factor (HCF) of A and B.

How did you do?

Did this page help you?

4a
Sme Calculator3 marks

Write 720 as a product of its prime factors.
Show your working clearly.

How did you do?

4b
Sme Calculator1 mark

Find the smallest whole number that 720 can be multiplied by to give a square number.

How did you do?

Did this page help you?

5a
Sme Calculator2 marks

Find the highest common factor left parenthesis HCF right parenthesis of 96 and 120.

How did you do?

5b
Sme Calculator2 marks

table row cell A space end cell equals cell space 2 cubed space cross times space 5 space cross times space 7 squared space cross times space 11 space end cell row cell B space end cell equals cell space 2 to the power of 4 space cross times space 7 space cross times space 11 space end cell row cell C space end cell equals cell space 3 space cross times space 5 squared end cell end table

Find the lowest common multiple left parenthesis LCM right parenthesis of A comma space B and C.

How did you do?

Did this page help you?

6
Sme Calculator2 marks

table row cell A space end cell equals cell space 3 to the power of 5 cross times space 5 space cross times space 7 cubed space end cell row cell B space end cell equals cell space 2 cubed cross times space 3 space cross times space 7 to the power of 4 space end cell row cell C space end cell equals cell space 2 to the power of p cross times space 5 to the power of q cross times space 7 to the power of r end cell end table

Given that

the HCF of B and C is 23× 7
the LCM of A and C is 24× 35× 52× 73

Find the value of p comma the value of q and the value of r.

p space equals ....................................................... 
q space equals ....................................................... 
r space equals ....................................................... 

How did you do?

Did this page help you?