Number
HCF and LCM
Find the highest common factor and the lowest common multiple of two numbers, and use them to answer sharing and repeating problems.
Two numbers usually share some factors. The largest one they share is called the highest common factor, or HCF. They also share multiples — every pair does, because multiplying the two numbers together always gives one. The smallest multiple they share is the lowest common multiple, or LCM.
Which one does a problem want?
If something is being cut up or shared into equal groups, you want the HCF: it is a factor, so it is never bigger than either number. If something keeps repeating and you are waiting for two cycles to line up, you want the LCM: it is a multiple, so it is at least as big as the larger number. Checking the size of your answer against that rule catches most mix-ups.
Have a play
Every mark here is a multiple of 4 and a multiple of 6 at the same time. Move from one to the next.
Tap anywhere on the line.
Worked example
Find the HCF of 18 and 24.
Factors of 18: 1, 2, 3, 6, 9, 18.
Written in pairs — 1 × 18, 2 × 9, 3 × 6 — so none gets missed.
Try it together
Now let us find the LCM of 8 and 12 together.
Multiplying them gives 96, and that is certainly a common multiple — but it is not the lowest one. Listing finds the real answer quickly.
1.List the multiples of 8: 8, 16, 24, 32. What is the fourth multiple of 12?
Have a go
Have a go on your own: what is the HCF of 20 and 30?
Hint: Both are in the same times table, and it is a two-digit one.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.