Logic Masters · Ages 11 to 12
LCM and HCF from Factor Trees
Match each number pair to its highest common factor or lowest common multiple. Five levels with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About LCM and HCF from Factor Trees
The highest common factor and the lowest common multiple are the two questions prime factorisation was invented to answer, and pupils who can factorise fluently still mix them up — usually because they were taught as procedures rather than as what the shared factors actually mean. This matching worksheet forces the distinction. Each row names a pair of numbers and asks for one of the two, and the answers are shuffled, so a pupil cannot work down the page applying the same operation to every line. The early levels ask only for the highest common factor, so that idea is secure on its own before the lowest common multiple appears alongside it; the upper levels mix both, and reading which is being asked becomes part of the task. Pairs sharing no common factor are excluded, since a highest common factor of one teaches nothing here. Every right-hand answer on a page is different, which matters because the matching is keyed by the displayed value — two rows with the same target would make both unanswerable. Each level prints as a clean A4 sheet with its own separate answer key. Its on-screen twin is LCM HCF Ladder Climb.
Common questions
- When does the LCM appear?
- From the third level. The early levels ask only for the HCF so that idea is secure on its own first.
- Are any pairs coprime?
- No. A pair with no common factor gives an HCF of one, which teaches nothing here, so those are excluded.
- Can two rows share the same answer?
- No. The matching is keyed by the displayed value, so every target on a page is different.
- Is an answer key included?
- Yes. Every level downloads with a key giving the correct letter and value for each row.
A hand for grown-ups
- Before you start
- Think of it as groups: "4 × 3" is four groups of three. Have something you can arrange into equal groups.
- While they work
- Skip-counting (3, 6, 9, 12…) is a solid way in before facts are memorised. Let them use it — speed comes later.
- Afterwards
- Spot arrays in real life together — eggs in a box, tiles on a floor. Rows-and-columns is multiplication you can see.
- Watch out for
- Treating it as harder addition and losing track. Grouping objects physically keeps the "equal groups" idea in view.
- Away from the screen
- Lay out objects in rows and columns and count them two ways. Cooking with doubled recipes is multiplication too.
Where to go next
Chosen by the skills this activity practises.