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4MA1/2FR Jun 2019, Question 23: HCF and LCM

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 4 marks

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The question, in short

Given A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11, work out the highest common factor and the lowest common multiple of the two numbers.

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Part (a) · 2 marks

Using the prime factorisations of A and B, determine the highest common factor of the two numbers.

  1. 1Take the lowest power of each common prime
  2. 2HCF = 3² × 5³ × 7
  3. 3= 9 × 125 × 7 = 7875

Answer7875

Part (b) · 2 marks

Using the prime factorisations of A and B, determine the lowest common multiple of the two numbers.

  1. 1Take the highest power of every prime
  2. 2LCM = 3⁴ × 5⁴ × 7 × 11
  3. 3= 81 × 625 × 77 = 3 898 125

Answer3898125

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