Lemmara logoLemmaraWorked solution

4024/11 Oct/Nov 2023, Question 14: HCF and LCM

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Write 36 as a product of prime factors, then use the 36-minute and 48-minute bus intervals, both starting at 09 30, to find when the buses next leave together.

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

Part (a) · 2 marks

Express 36 as a product of its prime factors.

  1. 136 = 2 × 18 = 2 × 2 × 9
  2. 2= 2 × 2 × 3 × 3 = 2² × 3²

Answer2 × 2 × 3 × 3 or 2² × 3²

Part (b) · 3 marks

Buses leave every 36 and 48 minutes from 09 30; find the next time both depart together.

  1. 136 = 2² × 3², 48 = 2⁴ × 3
  2. 2LCM = 2⁴ × 3² = 144 minutes = 2 h 24 min
  3. 309 30 + 2 h 24 min = 11 54

Answer11 54

Stuck on a step? Read the free lesson: HCF and LCM

Practise more hcf and lcm questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on hcf and lcm

Also searched as: 4024/11/O/N/23 · 4024_w23_qp_11 · 4024 w23 11 · question 14.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.