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Grade 4 · Foundation and Higher · free GCSE maths worksheet

HCF and LCM using prime factors

Using prime factor decomposition.

17 original questions, 49 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 the lowest common multiple (LCM) of

3    6    9    18    54

1 mark
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54
2

Find the lowest common multiple (LCM) of 8 and 12.

2 marks
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24
3

A bus to Hull leaves a station every 12 minutes. A bus to York leaves the same station every 18 minutes. Both buses leave at 08:00.

At what time do they next leave together?

2 marks
Show answer
08:36
4
  1. Write 84 as a product of its prime factors.
  2. Write 126 as a product of its prime factors.
  3. Find the highest common factor (HCF) of 84 and 126.
  4. Find the lowest common multiple (LCM) of 84 and 126.
5 marks
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a) 2² × 3 × 7 b) 2 × 3² × 7 c) 42 d) 252
5

A = 23 × 32 × 5   and   B = 22 × 3 × 7

  1. Find the highest common factor of A and B.
  2. Find the lowest common multiple of A and B.

Give both answers as ordinary numbers.

3 marks
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a) 12 b) 2520
6

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

2 marks
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18
7

The prime factors of 60 and 90 have been sorted into a Venn diagram, shown here as a table.

Only in 60In bothOnly in 90
22   3   53
  1. Use the diagram to find the HCF of 60 and 90.
  2. Use the diagram to find the LCM of 60 and 90.
3 marks
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a) 30 b) 180
8

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

2 marks
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12
9

The highest common factor of two numbers is 12 and their lowest common multiple is 72. One of the numbers is 36.

Work out the other number.

3 marks
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24
10

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

2 marks
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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

A = 23 × 3 × 52

B = 22 × 32 × 5

  1. Find the highest common factor (HCF) of A and B.
  2. Find the lowest common multiple (LCM) of A and B.

    Give your answers as products of powers of primes.

3 marks
Show answer
a) 22 x 3 x 5 = 60 b) 23 x 32 x 52 = 1800
13

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
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candles) 4 packs holders) 3 packs
14

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
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120 seconds
15
  1. Write 126 as a product of its prime factors.
  2. Find the lowest common multiple (LCM) of 126 and 60
4 marks
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a) 2 x 32 x 7 b) 1260
16
  1. Write 448 as a product of powers of its prime factors.
  2. Find the highest common factor (HCF) of 448 and 168
4 marks
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a) 26 x 7 b) 56
17
  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.

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