If you have worked through Factors and multiples, you will know that the factors of a number are all the numbers that divide into it. In this Revision Bite we are going to look at HCF and LCM.
Highest common factor and lowest common multiple
We can use prime factors to find the highest common factor (HCF) and lowest common multiple (LCM).
Highest common factor
Here are the list of prime factors of 24 and 36:
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
If we write down the numbers that are the same in both lists, they will give us the highest common factor of 24 and 36:
HCF of 24 and 36 is 2 x 2 x 3 = 12
Lowest common multiple
To find the lowest common multiple, we need to think about which list has the most of each factor.
24 = (2 x 2 x 2) x (3)
36 = (2 x 2) x (3 x 3)
24 has the most 2s. (it has three 2s). And 36 has the most 3s (it has two 3s).
So the LCM of 24 and 36 is (2 x 2 x 2) x (3 x 3) = 72.
- Question
Find the HCF and LCM of 90 and 175.
- Answer
90 = 2 x 3 x 3 x 5
175 = 5 x 5 x 7
HCF = 5
To find the LCM we group the prime factors using brackets.
90 = (2) x (3 x 3) x (5)
175 = (5 x 5) x (7)
LCM = 2 x (3 x 3) x (5 x 5) x 7 = 3150
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