Question

Find the smallest possible integer m such that 54m is a cube number?

Answer 1

`m=4`

Explanation:

`54=2*3^3`

`root(3)(54m)=root(3)(2*3^3m)`

`=3root(3)(2m)`

least cubic numbers are `1 and 8`

but `1` is not possible as `m` must be an integer

So,

`2m=8` `color(green)(rarr` `m=4`

`54*4=216`
`216=6^3`