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4MA1/1FR Jan 2022, Question 20: HCF and LCM

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 4 marks

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The question, in short

Find the LCM of 36 and 120, then use the prime factor forms of A and B with m > 2, n > 10, p > 1 to find their HCF as a product of prime powers.

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Part (a) · 2 marks

Work out the lowest common multiple of 36 and 120.

  1. 136 = 2² × 3² and 120 = 2³ × 3 × 5
  2. 2The LCM takes the highest power of each prime: 2³ × 3² × 5
  3. 38 × 9 × 5 = 360

Answer360

Part (b) · 2 marks

Using A = 5² × 7⁴ × 11ᵖ and B = 5ᵐ × 7ⁿ⁻⁵ × 11, find the HCF of A and B as a product of powers of primes.

  1. 1The HCF takes the lower power of each prime
  2. 2For 5, m > 2 so it is 5²; for 7, n − 5 > 5 so it is 7⁴
  3. 3For 11, p > 1 so it is 11¹
  4. 4HCF = 5² × 7⁴ × 11

Answer5² × 7⁴ × 11

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