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4MA1/2HR Jun 2019, Question 8: HCF and LCM

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks

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The question, in short

Given two numbers written as products of prime powers, work out their highest common factor and their lowest common multiple.

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Part (a) · 2 marks

Using A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11, determine the HCF.

  1. 1HCF uses the lowest power of each prime in both: 3², 5³ and 7
  2. 23² × 5³ × 7 = 9 × 125 × 7 = 7875

Answer7875

Part (b) · 2 marks

For the same A and B, determine the LCM.

  1. 1LCM uses the highest power of every prime: 3⁴, 5⁴, 7 and 11
  2. 23⁴ × 5⁴ × 7 × 11 = 81 × 625 × 77 = 3898125

Answer3898125

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