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4024/21 May/Jun 2024, Question 4: HCF and LCM

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

Find a square-number factor of 50 other than 1, then use prime factor forms of A and B to express their HCF and LCM in terms of x and y.

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Part (a) · 1 mark

Identify the square number, apart from 1, that divides 50.

  1. 150 = 2 × 5², factors include 1 and 25
  2. 225

Answer25

Part (bi) · 2 marks

Using the prime factor forms of A and B, give the HCF in terms of x and y.

  1. 1Take the lower power of each common prime: 2^(x − 1) and 3ʸ
  2. 2HCF = 2^(x − 1) × 3ʸ

Answer2^(x − 1) × 3ʸ

Part (bii) · 2 marks

Using the prime factor forms of A and B, give the LCM in terms of x and y.

  1. 1Take the higher power of every prime: 2^(x + 3), 3^(2y), 5, 7
  2. 2LCM = 2^(x + 3) × 3^(2y) × 5 × 7

Answer2^(x + 3) × 3^(2y) × 5 × 7

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Also searched as: 4024/21/M/J/24 · 4024_s24_qp_21 · 4024 s24 21 · question 4.
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