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Linear sequences

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HCF and LCM

The factors of a number are any numbers that divide into it exactly.

Highest Common Factor (HCF)

The factors of 12 are 1, 2, 3, 4, 6 and 12
The factors of 18 are 1, 2, 3, 6, 9 and 18

1, 2, 3 and 6 are factors of both 12 and 18.
They are known as the common factors of 12 and 18.

So the Highest Common Factor (HCF) of 12 and 18 is 6.

Question

What is the HCF of 24 and 30?

Answer

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

So the HCF of 24 and 30 is 6.

Lowest Common Multiple (LCM)

The multiples of a number are all the numbers that it will divide into.

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ...
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ...

12, 24, and 36 are multiples of both 4 and 6 and are known as the common multiples of 4 and 6.

The lowest number that is a multiple of 4 and 6 is 12. So the LCM of 4 and 6 is 12.

Question

What is the LCM of 5 and 8?

Answer

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40...

The mulitples of 8 are 8, 16, 24, 32, 40, 48, 56...

So the LCM of 5 and 8 is 40.

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