If n is positive even integer, then n(n + 1)(n + 2) is divisible by _______. 

Let us consider different even values of n (as specified), starting from 2.

When n = 2, n(n + 1)(n + 2) = 2 × 3 × 4 = 24, which is divisible by 24 

When n = 4, n(n + 1)(n + 2) = 4 × 5 × 6 = 120, which is divisible by 24 

When n = 6, n(n + 1)(n + 2) = 6 × 7 × 8 = 336, which is divisible by 24 and so on 

So, if n is positive even integer, then n(n + 1)(n + 2) is divisible by 24.