Question

How do you derive GCF ?

Answer 1

The GCF is the largest prime factors that all the numbers being considered contain.

Explanation:

The GCF is the largest prime factors that all the numbers being considered contain:

`12=2*2*3`
`6=2*3`

for example 6 and 12 have a GCF of 3 but if you consider 12, 6 and 10 the GCF is 2. Some numbers like 7 and 11 have no common factors.

`10=2*5`

The least common multiple LCM is different and more useful:

`12=2*2*3`
`8=2*2*2`
`10=2*5`

Our LCM will need to include `2*2*3` for the `12` and then `2*2*2` for the `8` but since we already have two `2`s we only need to add one more: `2*2*2*3`, finally it will need a `2` and a `5` for the `10` but since the `2` is already in there we only need to add the `5`, so we get: `2*2*2*3*5`.

Therefore the LCM of 12, 8 and 10 is 120