If three positive numbers are consecutive multiples of 8 8, what's the largest number the product must be a multiple of?

GRE Quant Problem Solving
1

I have watched this video 3 times, looked up the solution etc and I don’t understand the reasoning behind this question. I understand multiplying the three smallest multiples of eight, but I don’t get why I’m doing that. For these questions am I just supposed to multiply the three smallest multiples and that’s my answer every time?

2

There’s no “smallest multiple,” though.

I’ll start you off:
The product of any three consecutive multiples of 8 can be expressed as (8t)(8t + 8)(8t + 16) for some integer t. Perhaps you can conclude something by factoring or doing something equivalent.