Question

What is the least common multiple of four and six?

Answer 1

LCM`=12`

Explanation:

We can simply list the multiples of 4 and 6:

`4: 4, 8, color(blue)12, 16, 20, 24, 28, 32, 36, 40, 44`
`6: 6, color(blue)12, 18, 24, 30, 36, 42, 48, 54, 60, 66`

We see that 12 is the lowest multiple that `4` and `6` have in common, so that would be our LCM.

Answer 2

It is `12`

Explanation:

A common multiple of `4` must have factors of `2xx2` (becasue `4` does) and also have factors of `2xx3` (as `6` does).

So any number whose factors inclus both `2xx2` and `2xx3` is a common multiple of `4` and `6`.

The least ( or smallest) common multiple has just `2xx2xx3`, so it is `12`

Answer 3

`LCM = 2xx2xx3 = 12`

Explanation:

If two numbers do not have any common factors, (excluding `1`) then their LCM is their product.

The LCM of `7 and 8` is `7xx8 = 56`
The LCM of `4 and 9` is `4 xx 9 = 36`

However if there is a common factor, then we have to avoid duplicating that factor.

`" "4= color(blue)(2)xx2`
`" "6 = color(blue)(2)" "xx3`

`LCM = color(blue)(2)xx2xx3 = 12`

In the LCM which is `12` :

there is `2xx2` which is the `4`
there is `2xx3` which is the `6`

So `12` has both `4 and 6` as factors.

`2xx2xx2xx3 = 24` would be a common multiple as well, but it not the lowest.