Lemmara logoLemmaraWorked solution

0580/31 Oct/Nov 2022, Question 4: HCF and LCM

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 12 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Find numbers with given properties, compute fractions, roots and powers, solve a car-hire cost for days, and find when two trains next depart together.

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

Part (ai) · 1 mark

Give a multiple of 3 lying between 70 and 80.

  1. 13 × 24 = 72, a multiple of 3 between 70 and 80

Answer72 or 75 or 78

Part (aii) · 1 mark

Give a factor of 63 that lies between 5 and 10.

  1. 163 = 7 × 9, so 7 is a factor between 5 and 10

Answer7 or 9

Part (aiii) · 1 mark

Give a cube number between 60 and 90.

  1. 14³ = 64, between 60 and 90

Answer64

Part (aiv) · 1 mark

State the reciprocal of 7.

  1. 1Reciprocal of 7 = 1/7

Answer1/7 or 0.143 or 0.1428…

Part (b) · 1 mark

Calculate 2/7 of 84.

  1. 184 ÷ 7 = 12, 12 × 2 = 24

Answer24

Part (ci) · 1 mark

Find the cube root of 3375.

  1. 115³ = 3375, so ∛3375 = 15

Answer15

Part (cii) · 1 mark

Find the value of 12 to the power 0.

  1. 1Any non-zero number to the power 0 is 1: 12⁰ = 1

Answer1

Part (d) · 2 marks

Car hire costs $74 per day plus $17.50 delivery; total $461.50. Find the number of days hired.

  1. 1(461.50 − 17.50) ÷ 74
  2. 2= 444 ÷ 74 = 6 days

Answer6

Part (e) · 3 marks

Trains leave every 25 and 45 minutes, both at 08 00. Find the next time both leave together.

  1. 125 = 5², 45 = 3² × 5
  2. 2LCM = 3² × 5² = 225 minutes = 3 h 45 min
  3. 308 00 + 3 h 45 min = 11 45

Answer11 45

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

Practise more hcf and lcm questions

Real 0580 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: 0580/31/O/N/22 · 0580_w22_qp_31 · 0580 w22 31 · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.