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0580/13 May/Jun 2026, Question 19: Prime Factorization

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Non-calculator · 4 marks

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The question, in short

Work with prime factorisations of 84 and 96, finding the exponent P and then the LCM of the two numbers as a product of primes.

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

Part (a) · 2 marks

Express 84 as a product of its prime factors.

  1. 184 = 2 × 42
  2. 242 = 2 × 21 = 2 × 3 × 7
  3. 384 = 2² × 3 × 7

Answer2² × 3 × 7

Part (b) · 1 mark

Given 96 = 2ᴾ × 3, find the value of P.

  1. 196 ÷ 3 = 32
  2. 232 = 2⁵
  3. 3P = 5

Answer5

Part (c) · 1 mark

Using the prime factorisations of 84 and 96, find their LCM, leaving it as a product of primes.

  1. 184 = 2² × 3 × 7, 96 = 2⁵ × 3
  2. 2Take the highest power of each prime
  3. 3LCM = 2⁵ × 3 × 7

Answer2⁵ × 3 × 7

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