# Finding the LCM and HCF of two numbers

How to work out the lowest common multiple and the highest common factor from prime numbers.

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## 1

Showing a number as a product of its prime factors means to use a prime number such as 2,5,7... and multiplying with another number (which can also be prime).

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## Showing a number as a product of its prime factors

Write 48 as a product of its prime factors...

48
/   \
24   2
/  \
2   12
/ \
4   3
/  \
2     2

Split each number up by finding two numbers which multiply together to make that number; like 2x24=48. Then highlight the prime numbers.

2 x 2 x 3 x 2 x 2 = 48

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## Showing a number as a product of its prime factors

180
/     \
90     2
/  \
2   45
/ \
9    5
/ \
3

2 x 2 x 5 x 3 x 3=180

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## Venn Diagram

We now put all of our prime numbers into a venn diagram.------------------------------------------->

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## Numbers

We have

2 x 2 x 2 x 2 x 3=48

and

2 x 2 x 3 x 3 x 5=180

The numbers which only come in 48 go in the '48' side of the venn diagram

All the numbers in 180 go in the '180' side

All the numbers which are common in both numbers go in the middle

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## HCF

To find the HCF of both 48 and 180 we multiply together the numbers which are in the middle section of the diagram, so...

2 x 2 x 3 = 12

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## LCM

To find the lowest common multiple, we multiply all the numbers together; so...

2 x 2 x 2 x 2 x 3 x 3 x 5 = 720

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