The product of three consecutive natural numbers is divisible by

Let n,n+1,n+2 be there consecutive natural number and let P(n) be their product. Then,P(n)=n(n+1)(n+2)We haveP(1)=1×2×3=6 which is divisible by 3 and 6P(2)=2×3×4=24, which is divisible by 3, 8 and  6P(3)=3×4×5=60 which is divisible by 3 and 6.P(4)=4×5×6=120 which is divisible by 3, 8 and 6.Hence, P(n) is divisible by 6 for all n ∈ N