Robinson Tuition
Grade 3 · Foundation · free GCSE maths worksheet

Highest common factor and lowest common multiple (listing)

Finding HCF and LCM by listing.

19 original questions, 45 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write down a factor of 20 that is greater than 5 and less than 20.

1 mark
Show answer
10
2

Write down all the factors of 18.

2 marks
Show answer
1, 2, 3, 6, 9, 18
3

Write down the lowest common multiple (LCM) of

3    6    9    18    54

1 mark
Show answer
54
4

Write down all the factors of 30.

2 marks
Show answer
1, 2, 3, 5, 6, 10, 15, 30
5

Find the highest common factor (HCF) of 54 and 90

2 marks
Show answer
18
6

Find the lowest common multiple (LCM) of 6 and 8.

2 marks
Show answer
24
7

Find the highest common factor (HCF) of 48 and 84

2 marks
Show answer
12
8

Write down all the numbers that are factors of both 24 and 40.

2 marks
Show answer
1, 2, 4, 8
9

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

2 marks
Show answer
36
10

Write down two numbers, both greater than 20, whose highest common factor (HCF) is 7

2 marks
Show answer
Any valid pair, e.g. 21 and 28 (21 = 3 x 7 and 28 = 4 x 7, and 3 and 4 share no common factor greater than 1, so HCF = 7).
11

Find the lowest common multiple (LCM) of 15 and 18

3 marks
Show answer
90
12

Find the highest common factor (HCF) of 28 and 42.

3 marks
Show answer
14
13

List all the factors of 28.

2 marks
Show answer
1, 2, 4, 7, 14, 28
14

A bus to the station leaves every 10 minutes. A bus to the market leaves every 25 minutes.

Both buses leave the bus stop together at 8:00 am.

At what time do they next leave together?

3 marks
Show answer
8:50 am
15

Nadia is making table decorations.

Each decoration needs one candle and one holder.

Candles are sold in packs of 9

Holders are sold in packs of 12

Nadia buys exactly the same number of candles as holders, with none left over.

Work out the smallest number of packs of candles and the smallest number of packs of holders she can buy.

3 marks
Show answer
candles) 4 packs holders) 3 packs
16

Ravi has 48 red counters and 36 blue counters.

He puts them into identical bags. Each bag has the same number of red counters and the same number of blue counters. No counters are left over.

What is the greatest number of bags Ravi can make?

3 marks
Show answer
12
17

Two warning buoys are anchored in a harbour.

One buoy flashes every 24 seconds.

The other buoy flashes every 40 seconds.

At 8 pm the two buoys flash at the same time.

Work out how many seconds later the two buoys next flash at the same time.

3 marks
Show answer
120 seconds
18

Work out how many positive whole numbers less than 100 are multiples of both 4 and 6.

3 marks
Show answer
8
19
  1. Find the highest common factor (HCF) of 72 and 120
  2. Find the lowest common multiple (LCM) of 72 and 120
4 marks
Show answer
a) 24 b) 360

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

All Grade 3 topics