Math Worksheets
LCM and HCF Worksheets
Find lowest common multiples and highest common factors.
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What this tool does
Generate printable LCM and HCF worksheets. Each problem gives a pair of numbers and asks for the highest common factor, the lowest common multiple, or both. Choose the mode and number range, with an answer key.
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16 pairs · HCF & LCM · up to 30
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Master LCM and HCF
Lowest common multiple (LCM) and highest common factor (HCF) are core number-theory skills used in adding fractions, simplifying ratios, and solving timing problems. This generator builds worksheets of number pairs and asks for the HCF, the LCM, or both. You control the number range and how many problems appear, and an answer key is produced automatically.
HCF and LCM explained
The highest common factor of two numbers is the largest number that divides into both — the HCF of 12 and 18 is 6. The lowest common multiple is the smallest number both divide into — the LCM of 12 and 18 is 36. A handy check: for any pair, HCF × LCM equals the product of the two numbers.
What you can customise
- Mode — HCF only, LCM only, or both for each pair.
- Number range — keep numbers small for an introduction or larger for a challenge.
- Problems per sheet — short practice or a full page.
- Answer key, Name & Date — for marking and classroom use.
How to use it
- Choose the mode (HCF, LCM, or both).
- Set the maximum number and how many problems you want.
- Toggle the answer key and Name/Date fields.
- Preview, then download or print the worksheet.
Teaching ideas
Introduce HCF and LCM with factor lists and multiple lists before moving to prime factorisation for larger numbers. Use the HCF × LCM = product rule as a self-check. Mixed (both) sheets make strong revision before tests on fractions and ratio.
FAQs
Quick answers
What is the difference between HCF and LCM?
The HCF (highest common factor) is the largest number that divides into both numbers; the LCM (lowest common multiple) is the smallest number both divide into. For 12 and 18, the HCF is 6 and the LCM is 36.
Is there a quick way to check my answers?
Yes — for any pair of numbers, the HCF multiplied by the LCM equals the product of the two numbers. If that holds, your answers are consistent.
Can I practise just one of them?
Yes. Choose HCF only, LCM only, or both. The 'both' mode asks for the HCF and LCM of each pair on one line.
What number range should I use?
Start with numbers up to 20–30 for an introduction. Increase the maximum for harder problems that benefit from prime factorisation.
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