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Prime factors, HCF & LCM practice questions with answers

Foundation and Higher · Grade 4 · Non-calculator

A second set of prime factors, HCF & LCM questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

Find the HCF of 8, 12 and 20.

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Answer: 4

  1. A common factor has to divide all three.
  2. The value is 4.
  • Method (1): A common factor has to divide all three.
  • Accuracy (1): Answer 4

Question 2 Easy

How many prime factors does 12 have, counted with repeats, in 2 × 2 × 3?

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Answer: 3

  1. 12 = 2 × 2 × 3.
  2. That is three prime factors.
  • Method (1): 12 = 2 × 2 × 3.
  • Accuracy (1): Answer 3

Question 3 Medium

Write 18/24 in its simplest form. What is the new numerator?

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Answer: 3

  1. The HCF of 18 and 24 is 6.
  2. Divide the numerator by 6.
  • Method (1): The HCF of 18 and 24 is 6.
  • Accuracy (1): Answer 3

Question 4 Medium

Find the LCM of 3, 4 and 5.

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Answer: 60

  1. Take the highest power of each prime.
  2. The value is 60.
  • Method (1): Take the highest power of each prime.
  • Accuracy (1): Answer 60

Question 5 Hard

Write the value of 2 × 3 × 5.

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Answer: 30

  1. Multiply the prime factors.
  2. The value is 30.
  • Method (1): Multiply the prime factors.
  • Accuracy (1): Answer 30

Question 6 Hard

Two numbers have HCF 2 and LCM 12. One number is 4. What is the other?

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Answer: 6

  1. HCF × LCM = the product of the two numbers.
  2. Divide by the known number.
  • Method (1): HCF × LCM = the product of the two numbers.
  • Accuracy (1): Answer 6

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

A bell rings every 5 minutes and another every 6 minutes. How many times do they ring together in 60 minutes, not counting the start?

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Answer: 2

  1. They ring together every 30 minutes.
  2. 60 ÷ 30 is the number of times after the start.
  • Method (1): They ring together every 30 minutes.
  • Method (1): 60 ÷ 30 is the number of times after the start.
  • Accuracy (1): Answer 2

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What is the highest common factor of 36 and 48?

  1. 12
  2. 144
  3. 1728
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12 The result is 12.

Check 2

What is the lowest common multiple of 36 and 48?

  1. 144
  2. 12
  3. 1728
Show answer

144 The result is 144.

Check 3

What is the highest common factor of 40 and 60?

  1. 20
  2. 120
  3. 2400
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20 The result is 20.

Check 4

What is the lowest common multiple of 40 and 60?

  1. 120
  2. 20
  3. 2400
Show answer

120 The result is 120.

Check 5

What is the highest common factor of 45 and 75?

  1. 15
  2. 225
  3. 3375
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15 The result is 15.

Check 6

What is the lowest common multiple of 45 and 75?

  1. 225
  2. 15
  3. 3375
Show answer

225 The result is 225.

Check 7

What is the highest common factor of 50 and 75?

  1. 25
  2. 150
  3. 3750
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25 The result is 25.

Check 8

What is the lowest common multiple of 50 and 75?

  1. 150
  2. 25
  3. 3750
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150 The result is 150.

Check 9

What is the highest common factor of 48 and 72?

  1. 24
  2. 144
  3. 3456
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24 The result is 24.

Check 10

What is the lowest common multiple of 48 and 72?

  1. 144
  2. 24
  3. 3456
Show answer

144 The result is 144.

Check 11

What is the highest common factor of 54 and 90?

  1. 18
  2. 270
  3. 4860
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18 The result is 18.

Check 12

What is the lowest common multiple of 54 and 90?

  1. 270
  2. 18
  3. 4860
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270 The result is 270.

Check 13

What is the highest common factor of 60 and 84?

  1. 12
  2. 420
  3. 5040
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12 The result is 12.

Check 14

What is the lowest common multiple of 60 and 84?

  1. 420
  2. 12
  3. 5040
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420 The result is 420.

Check 15

What is the highest common factor of 72 and 120?

  1. 24
  2. 360
  3. 8640
Show answer

24 The result is 24.

Keep going with Prime factors, HCF & LCM

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