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4MA1/2FR Jan 2023, Question 21: HCF and LCM

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

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The question, in short

Find the HCF of 200 and 420, then find the LCM of A, B and C given as prime factor products, leaving the LCM in prime power form.

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Part (a) · 2 marks

Find the highest common factor of 200 and 420.

  1. 1200 = 2 × 2 × 2 × 5 × 5
  2. 2420 = 2 × 2 × 3 × 5 × 7
  3. 3Common prime factors: 2, 2, 5
  4. 4HCF = 2 × 2 × 5 = 20

Answer20

Part (b) · 2 marks

Using A = 2³ × 3 × 5 × 7², B = 2 × 3² × 7, C = 3 × 5² × 11, find the LCM as a product of prime powers.

  1. 1A = 2³ × 3 × 5 × 7²
  2. 2B = 2 × 3² × 7
  3. 3C = 3 × 5² × 11
  4. 4LCM takes highest power of each prime:
  5. 52³, 3², 5², 7², 11
  6. 6LCM = 2³ × 3² × 5² × 7² × 11

Answer2³ × 3² × 5² × 7² × 11

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