Prove: The product of any three consecutive integers is divisible by $6$. I'm new to number theory and was wondering if someone could help me with this proof. 
Prove: The product of any three consecutive integers is divisible by $6$. 
So far I have $\cfrac{x(x+1)(x+2)}{6}$; How would I go about proving this? Should I replace $x$ with $k$ and then $k$ with $k+1$ and see if the statement is true?

Hint $\displaystyle\ \ n(n\!+\!1)(n\!+\!2)\, =\, 6 { n+2 \choose 3}$
