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Factors, multiples and primes

HCF and LCM

64 self-marking GCSE and IGCSE practice questions on HCF and LCM, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Instant marking with full worked solutions on every question.

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Sample HCF and LCM questions

A few of the 64 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

Question 11 markGrade 2
Work out the lowest common multiple (LCM) of 20, 30 and 40. Circle your answer: 10, 120, 240, 24000
Show the worked solution
20=2²×5, 30=2×3×5, 40=2³×5.
LCM = 2³×3×5 = 120.
Question 22 marksGrade 4
Doctor Jones starts an appointment every 20 minutes. Doctor Warholm starts an appointment every 35 minutes. The first appointment for both doctors starts at 8.30 am. What is the next time that they both have an appointment start at the same time?
Show the worked solution
LCM(20, 35): 20 = 2² × 5, 35 = 5 × 7. LCM = 2² × 5 × 7 = 140 minutes. M1
140 minutes = 2 hours 20 minutes.
8:30 am + 2:20 = 10:50 am. A1
Question 32 marksGrade 5-6

What are the common mistakes in HCF and LCM?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

Uses the highest common factor where the lowest common multiple was needed
Found the highest common FACTOR (1) instead of the lowest common MULTIPLE - check which one the question actually asks for
Takes the lowest shared power of each prime factor instead of the highest when finding the LCM
Took the LOWEST shared power of each prime (giving the HCF, 24) instead of the HIGHEST - for the LCM, take the highest power of each prime appearing in either factorisation
Multiplies the two numbers together instead of finding their highest common factor
Multiplied 10 × 12 = 120 instead of finding their highest common factor

Quick answers about HCF and LCM

How many HCF and LCM practice questions are there?: There are 64 self-marking GCSE and IGCSE Maths questions on HCF and LCM, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise HCF and LCM?: No. You can start practising HCF and LCM straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.