Question

Question #51c21

Answer 1

60

Explanation:

The lowest common multiple is the lowest number which has all of these numbers as factors. Looking at the individual factors...

`5` is prime
`6` factors into `2*3=6`
`20` factors into `2*2*5 = 20`

In order to find a multiple of `20` that is also a multiple of our other numbers, consider the factors. If we multiplied 5 by 6, the resulting number (30) would factor into (2,3,5). 20 already has the 2 and the 5, but not the 3; thus, if we multiply 20 by 3...

`3*20 = 3*2*2*5 = 60`

Now, we have (2, 2, 3, 5). This set of factors contains both the factors of 5 and the factors of 6.

You might ask why we can't simply remove one of the 2s in our set of factors. If we removed one of them, then we would have (2,3,5), but 20 needs (2,2,5); we would be missing a necessary 2 from our factor list, and thus we cannot remove the 2 i nquestion.