Question

Question #99831

Answer 1

The LCM is `80`

Explanation:

Factor each number:

`16 = 2*2*2*2 = 2^4`

`20 = 2*2*5=2^2*5`

Every multiple of `16` has factors that include `2^4`

Every multiple of `20` has factors that include `2^2*5`.

The Least Common Multiple must include factors of `2^4`, `2^2` and `5` and no extra factors (otherwise it wouldn't be "least")

The least number that includes these is `2^4*5 = 80`

Answer 2

`LCM = 2xx2xx2xx2xx5 = 80`

Explanation:

The LCM must be divisible by `16 and 20`

Write each number as the product of its prime factors:

`" "16 =2xx2xx2xx2`
`" "ul(20= 2xx2color(white)(xxxxxx)xx5)`
`LCM = 2xx2xx2xx2xx5 = 80`

`80` now contains all the factors of `16 and 20` but without any duplicates,