Is this official?
It seems that it COULD be divisible by all 3.
It doesn't have to, however, depends on the value of m.
In algebraic way, in order for it to be divisible by 3, one of the factors (m or m+4 or m+5) needs to be divisible by 3, and for every possible positive integer, it will be.
For 6, it needs to be divisible by 2 and 3, in other words, have a factor of 2 and a factor of 3. We can see that for every value of m, either m+4 or m+5 will be even, thus divisible by 2 and, since it is also divisible by 3, be divisible by 6.
In order to be divisible by 4, it needs 2 be divisible by 2 twice, or that 2 out of our 3 factors (m, m+4, m+5) will be even. It is possible if m is even (e*e*o=e), if m is odd we get (o*e*o=e), so in any case it will be divisible by 2 but only when m is even it will be divisible by 4.
I don't know whether it fits the answer though, how should the word "could" be approached?
