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4024/11 Oct/Nov 2021, Question 14: HCF and LCM

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Express 60 as a product of primes, then find the smallest numbers of 60-pen packs and 42-ruler packs giving equal totals of pens and rulers.

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

Part (a) · 2 marks

Write 60 as a product of its prime factors.

  1. 160 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5
  2. 260 = 2² × 3 × 5

Answer2 × 2 × 3 × 5 or 2² × 3 × 5

Part (b) · 3 marks

Packs hold 60 pens or 42 rulers; find the least number of each pack so pen and ruler totals match.

  1. 142 = 2 × 3 × 7
  2. 2LCM of 60 and 42 = 2² × 3 × 5 × 7 = 420
  3. 3Packs of pens = 420 ÷ 60 = 7, packs of rulers = 420 ÷ 42 = 10
  4. 47 packs of pens, 10 packs of rulers

Answer7 packs of pens, 10 packs of rulers

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Also searched as: 4024/11/O/N/21 · 4024_w21_qp_11 · 4024 w21 11 · question 14.
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