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4024/12 May/Jun 2020, Question 13: Prime Factorization

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Write 108 as a product of prime factors, then find the lowest common multiple of 108 and 180.

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

Part (a) · 2 marks

Express 108 as a product of its prime factors.

  1. 1108 = 2 × 54 = 2 × 2 × 27 = 2 × 2 × 3 × 3 × 3
  2. 2108 = 2² × 3³

Answer2 × 2 × 3 × 3 × 3 or 2² × 3³

Part (b) · 2 marks

Find the lowest common multiple of 108 and 180.

  1. 1108 = 2² × 3³
  2. 2180 = 2² × 3² × 5
  3. 3LCM takes the highest power of each prime: 2² × 3³ × 5
  4. 4LCM = 4 × 27 × 5 = 540

Answer540

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Also searched as: 4024/12/M/J/20 · 4024_s20_qp_12 · 4024 s20 12 · question 13.
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