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4MA1/1H Jun 2018, Question 8: HCF and LCM

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Given A = 3⁵ × 5 × 7³ and B = 2³ × 3 × 7⁴, find the HCF and LCM of A and B, then use C = 2ᵖ × 5^q × 7ʳ with given HCF and LCM conditions to find p, q, r.

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Part (ai) · 1 mark

Find the Highest Common Factor of A and B from their prime factorisations.

  1. 1Common prime factors of A and B are 3 and 7
  2. 2Take the lower power of each: 3¹ and 7³
  3. 3HCF = 3 × 7³

Answer3 × 7³

Part (aii) · 1 mark

Find the Lowest Common Multiple of A and B from their prime factorisations.

  1. 1Prime factors in A or B are 2, 3, 5 and 7
  2. 2Take the higher power of each: 2³, 3⁵, 5¹, 7⁴
  3. 3LCM = 2³ × 3⁵ × 5 × 7⁴

Answer2³ × 3⁵ × 5 × 7⁴

Part (b) · 2 marks

Using C = 2ᵖ × 5^q × 7ʳ, the HCF of B and C, and the LCM of A and C, find p, q and r.

  1. 1B has 7⁴ but the HCF of B and C has only 7¹, so r = 1
  2. 2A has no 2, but the LCM of A and C has 2⁴, so p = 4
  3. 3A has 5¹, but the LCM has 5², so q = 2
  4. 4p = 4, q = 2, r = 1

Answerp = 4, q = 2, r = 1

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