LCM and HCF Worksheets

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

1. Choose the mode (HCF, LCM, or both).
2. Set the maximum number and how many problems you want.
3. Toggle the answer key and Name/Date fields.
4. 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.