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4MA1/1HR Jan 2021, Question 9: HCF and LCM

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

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The question, in short

Given A = 2⁸ × 3⁵ × 11⁴ and B = 2⁶ × 3 × 11⁸, find the HCF of A and B, then the LCM of 2A and 3B as a product of prime powers.

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Part (a) · 2 marks

Find the highest common factor of A and B.

  1. 1For the HCF take the lowest power of each prime in both
  2. 22: lowest of 2⁸ and 2⁶ is 2⁶; 3: lowest of 3⁵ and 3 is 3; 11: lowest is 11⁴
  3. 3HCF = 2⁶ × 3 × 11⁴

Answer2⁶ × 3 × 11⁴

Part (b) · 2 marks

Find the lowest common multiple of 2A and 3B, giving it as a product of powers of prime factors.

  1. 12A = 2⁹ × 3⁵ × 11⁴ and 3B = 2⁶ × 3² × 11⁸
  2. 2For the LCM take the highest power of each prime
  3. 3LCM = 2⁹ × 3⁵ × 11⁸

Answer2⁹ × 3⁵ × 11⁸

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