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.

Which one the question actually wants

Children reliably confuse these two, and the confusion is usually about the words rather than the method.

HCF — highest common factor. Factors divide into a number, so the HCF is never larger than the smaller of the two numbers. It is about splitting things up.

LCM — lowest common multiple. Multiples are what you get counting up, so the LCM is never smaller than the larger of the two numbers. It is about things coinciding.

That size check is the most useful thing to teach: an HCF bigger than either number, or an LCM smaller than either, is definitely wrong. It catches the confusion without needing to re-explain the definitions.

Two reliable methods

Listing works for small numbers and builds understanding. Write the factors of both and take the largest shared one; or write the multiples of both and take the first shared one. Slow, transparent, and the right place to start.

Prime factorisation scales to larger numbers. Break both into primes, then:

• HCF — multiply the primes appearing in both, taking the lower power of each.
• LCM — multiply every prime appearing in either, taking the higher power.

For 12 = 2² × 3 and 18 = 2 × 3²: the HCF is 2 × 3 = 6, and the LCM is 2² × 3² = 36.

A useful check: HCF × LCM equals the product of the two numbers. Here 6 × 36 = 216, and 12 × 18 = 216.

Word problems, and how to spot which is needed

Exam questions rarely use the terms, so the skill is recognising the situation.

HCF situations involve splitting into equal groups with nothing left over. "What is the largest number of identical party bags I can make from 24 sweets and 36 stickers?" — the answer is the HCF, 12.

LCM situations involve two repeating events coinciding. "One bus comes every 12 minutes and another every 18. They have just both arrived — when will that happen again?" — the LCM, 36 minutes.

The tell: if the question is dividing something up, it wants the HCF. If it is waiting for things to line up, it wants the LCM. Sorting a set of word problems into those two piles, without solving any of them, is a genuinely useful exercise.

Where this is used later

Both ideas reappear, which is worth knowing while the practice feels abstract.

LCM is the common denominator. Adding ¹⁄₄ and ¹⁄₆ means finding the LCM of 4 and 6, which is 12. Children who have practised LCM find unlike-denominator addition considerably easier, and the connection is rarely pointed out to them.

HCF is cancelling. Simplifying ¹⁸⁄₂₄ to ³⁄₄ is dividing both parts by their HCF, 6. The same operation reappears in algebra when factorising expressions.

Mentioning these links while teaching the topic gives it a purpose beyond the sheet, and it makes the fraction work later feel like a continuation rather than a new problem.