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4MA1/1F Jun 2023, Question 23: Prime Factorization

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

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The question, in short

Write 300 as a product of primes, then use the given prime factorisations of A and B to find the LCM of 5A and 7B, showing working.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Express 300 as a product of its prime factors, showing the working clearly.

  1. 1300 = 2 × 150
  2. 2150 = 2 × 75
  3. 375 = 3 × 25
  4. 425 = 5 × 5
  5. 52 × 2 × 3 × 5 × 5

Answer2 × 2 × 3 × 5 × 5

Part (b) · 2 marks

Using A = 2 × 2 × 2 × 3 × 3 × 5 and B = 2 × 2 × 3 × 3 × 3 × 5, find the LCM of 5A and 7B, showing working.

  1. 15A = 5 × (2 × 2 × 2 × 3 × 3 × 5) = 2 × 2 × 2 × 3 × 3 × 5 × 5
  2. 27B = 7 × (2 × 2 × 3 × 3 × 3 × 5) = 2 × 2 × 3 × 3 × 3 × 5 × 7
  3. 3LCM takes highest powers: 2³ × 3³ × 5² × 7
  4. 48 × 27 × 25 × 7 = 37800

Answer37800

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