Find the HCF and LCM
When finding the HCF and LCM of relatively low/easy numbers we can use the
methods that we are used to such as find the HCF and LCM of 12 and 18
HCF
12
1 x 12
2x6
3x4
Factors are:
1,2,3,4,6 and 12
LCM
18
1 x 18
2x9
3x6
List all the multiples of both numbers
12,24,36,48,60,72,84,96,108…
18,36,54,72,90,108…
Common multiples are 36,72,108 …..
1,2,3,6,9 and 18
LCM is 36
Common factors are:
1,2,3,6
HCF is 6
With harder numbers such as 36 and 90 we would literally be here all day working
them out as these are larger numbers that we are not really used to so we have an
easier method for these types of numbers. The other way is still correct but it just
takes too long
Step 1
Split the numbers up to a product of prime numbers e.g.
36
3
12
3
4
Because 3 x 12 is equal to 36. We would circle or highlight
the 3 as this is a prime number but 12 is not so we would
split that again into 3 x 4. the three is a prime so we would
circle or highlight that as it can not be split up further, finally
we can split the 4 into 2 x 2 leaving the number 36 as a
product of prime numbers
36 = 3 x 3 x 2 x 2
2
2
or 3² x 2²
No matter which way we split it we will always end
up with the same answer as a product of prime numbers…
see the next slide.
36
36
2
6
18
2
3
9
3
36 = 3 x 3 x 2 x 2
6
2
2
3
3
or 3² x 2²
So no matter which way we do the working out we will always end up
with the same answer.
We could work out the product of prime
numbers for 90 in the same way.
90
2
90 = 2 x 5 x 3 x 3
45
5
We can check the calculation by first
seeing if they are all prime which they are
and finally checking that these numbers
do multiply to give 90… which they do
9
3
3
Step 2 – Put the product of prime numbers in a Venn diagram
90 = 2 x 5 x 3 x 3
36 = 2 x 2 x 3 x 3
36
90
2
5
3
2
3
These are the prime
numbers that is extra
in the product of 90
These are the prime
numbers that is extra
in the product of 36
These are the prime
numbers that both
numbers share so they go
in the middle
36
90
2
5
3
2
3
In order to find the HCF we multiply everything in the middle section.
2 x 3 x 3 = 18 which is the HCF
In order to find the LCM we multiply all the numbers in the Venn diagram together
5 x 2 x 3 x 3 x 2 = 180 which is the LCM
Try this method with an even more difficult
question
What is the HCF and LCM of:
a) 36 and 48 (try the Venn diagram method
although you can probably do it without)
b) 45 and 70
c) 110 and 125