The highest common factor (HCF) of two numbers is the biggest number that divides both. List the factors of each and find the largest on both lists. The lowest common multiple (LCM) is the smallest number both divide into. List multiples of the larger number until you reach one the smaller number also divides. HCF answers 'largest equal groups' questions; LCM answers 'when will they happen together again' questions.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- common factor
- a number that divides both numbers
- common multiple
- a number both numbers divide into
Worked examples
The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 18 are 1, 2, 3, 6, 9, 18. What is the highest common factor of 12 and 18?
- 1.The common factors are 1, 2, 3 and 6.
- 2.The highest is 6.
= 6
What is the lowest common multiple of 12 and 18?
- 1.Multiples of 18: 18, 36.
- 2.12 divides 36, so 36 is the first common multiple.
= 36
One light flashes every 6 seconds and another flashes every 8 seconds. They flash together now. After how many seconds will they next flash together?
- 1.They flash together at common multiples of 6 and 8.
- 2.Multiples of 8: 8, 16, 24. 6 divides 24.
= 24
For parents
Method: List and compare
What to say: Are we sharing into equal groups (HCF) or waiting until things line up (LCM)?
Common mistakes:
- Gives the lowest common multiple when asked for the highest common factor.
- Gives the highest common factor when asked for the lowest common multiple.
- Multiplies the two numbers to get the LCM, even when they share a factor.
- Gives a common factor, but not the highest one.
- Gives the smaller number as the HCF, assuming it must go into the larger.
- Gives the larger number as the LCM, assuming the smaller must go into it.