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4024/11 Oct/Nov 2020, Question 24: HCF and LCM

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

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The question, in short

Prime factor questions: write 99 as a product of primes, then use p = 2ⁿ⁺² × 3ⁿ × 5 and q = 2ⁿ × 3ⁿ⁺¹ × 5² with n a positive integer to find R and factorise p + q.

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Part (a) · 1 mark

Write 99 as a product of its prime factors.

  1. 199 = 9 × 11 = 3 × 3 × 11
  2. 2= 3² × 11

Answer3² × 11 or 3 × 3 × 11

Part (bi) · 2 marks

Given LCM of p and q equals 2ⁿ × 3ⁿ × R, express R as a product of prime factors.

  1. 1LCM takes the highest powers: 2ⁿ⁺² × 3ⁿ⁺¹ × 5²
  2. 2= 2ⁿ × 3ⁿ × 2² × 3 × 5²
  3. 3R = 2² × 3 × 5²

Answer2² × 3 × 5²

Part (bii) · 2 marks

Express p + q as a product of prime factors.

  1. 1p + q = 2ⁿ × 3ⁿ × (2² × 5 + 3 × 5²)
  2. 2= 2ⁿ × 3ⁿ × (20 + 75) = 2ⁿ × 3ⁿ × 95
  3. 3= 2ⁿ × 3ⁿ × 5 × 19

Answer2ⁿ × 3ⁿ × 5 × 19

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Also searched as: 4024/11/O/N/20 · 4024_w20_qp_11 · 4024 w20 11 · question 24.
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