Find the smallest integer $\displaystyle n, n > 2$, such that $\displaystyle 2 | n, 3 | (n+1), 4 | (n+2), 5 | (n+3)$, and $\displaystyle 6 | (n+4)$.

I know how to solve Linear Congruences and I can use the Chinese Remainder Theorem. Just not sure how to set this up as a system of linear congruences. Any help to start me off would be appreciated.