Question

Question #8a3cc

Answer 1

`120`

Explanation:

`color(white)(.....)8` `color(white)(123456789)` `12` `color(white)(123456789)` `15`
`...............` `color(white)(129)` `............` `color(white)(1298)` `.............`
`color(white)(.....)8` `color(white)(..............)12` `color(white)(................)15`
`color(white)(.....)16` `color(white)(.............)24` `color(white)(................)30`
`color(white)(.....)24` `color(white)(.............)36` `color(white)(................)45`
`color(white)(.....)32` `color(white)(.............)48` `color(white)(................)60`
`color(white)(.....)40` `color(white)(.............)60` `color(white)(................)75`
`color(white)(.....)48` `color(white)(.............)72` `color(white)(................)90`
`color(white)(.....)56` `color(white)(.............)84` `color(white)(................)105`
`color(white)(.....)64` `color(white)(.............)96` `color(white)(................)color(green)(120)`
`color(white)(.....)72` `color(white)(.............)108` `color(white)(................)color(white)(30)`
`color(white)(.....)80` `color(white)(.............)color(green)(120)` `color(white)(................)color(white)(30)`
`color(white)(.....)88` `color(white)(.............)color(white)(24)` `color(white)(................)color(white)(30)`
`color(white)(.....)96` `color(white)(.............)color(white)(24)` `color(white)(................)color(white)(30)`
`color(white)(.....)104` `color(white)(.............)color(white)(24)` `color(white)(................)color(white)(30)`
`color(white)(.....)112` `color(white)(.............)color(white)(24)` `color(white)(................)color(white)(30)`
`color(white)(.....)color(green)(120)` `color(white)(.............)color(white)(24)` `color(white)(................)color(white)(30)`

The LCM is `120`

Answer 2

`120`

Explanation:

The easiest way to do this is to find the prime factorization of each number first.

`8 = 4 * 2`
`8 = 2 * 2 * 2`
`8 = 2^3`

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

`15 = 5 * 3`

Now that we have reduced all numbers to their prime factorizations, we will look for the factors with the highest exponent and multiply them all together to get our LCM.

There is `2^3` from `8`, `3^1` from `12` and `15`, and `5^1` from `15`.

So now we must do the following:

`2^3 * 3 * 5`
`2 * 2 * 2 * 3 * 5`
`120`

Therefore, the LCM of `8`, `12`, and `15` is `120`.