Help if anyone can provide it! I'm stuck on a problem that I have the answer but don't know how they got it. Here it is:

A wire is cut into three equal parts. The resulting segments are then cut into 4, 6, and 8 parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire?

The answer is 72. But the rationale for why was explained and I don't understand.

I do understand why each piece must be "able" to be cut into pieces of 8 and would therefore would be 24 inches (8 x 3) but how does this end up being 72? Or, how and why does this get muliplied by 3? I think it has do do with multiples but its not sinking in.

Thanks,

Rob