Product of three consecutive integers is divisible by ………..

Product of three consecutive integers = odd even odd

Or Product of three consecutive integers = even odd even

In both the cases atleast one is even.

So, It is divisible by 2

Also, in three consecutive integers one of them is a multiple of 3.

Also, 2&3 are mutually prime numbers.

So, product of three consecutive integers is divisible by 6.