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4024/22 Oct/Nov 2025, Question 14: HCF and LCM

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 4 marks

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The question, in short

Given N = 2 × 3ˣ × 5ʸ and LCM of N and 360 is 16200, find x, y, the HCF of N and 360, and smallest k making kN a cube.

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Part (a) · 2 marks

Find the values of x and y using the given LCM of N and 360.

  1. 116 200 = 2³ × 3⁴ × 5², 360 = 2³ × 3² × 5
  2. 2The LCM takes the highest powers, and 360 only has 3² and 5¹, so N must give 3⁴ and 5²
  3. 3x = 4, y = 2

Answerx = 4, y = 2

Part (b) · 1 mark

Find the highest common factor of N and 360.

  1. 1N = 2 × 3⁴ × 5², 360 = 2³ × 3² × 5
  2. 2HCF = 2 × 3² × 5 = 90

Answer90

Part (c) · 1 mark

Find the smallest positive integer k so that kN is a cube number.

  1. 1N = 2 × 3⁴ × 5²; for a cube every power must be a multiple of 3
  2. 2Need 2³ × 3⁶ × 5³, so k = 2² × 3² × 5
  3. 3k = 4 × 9 × 5 = 180

Answer180

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