Consecutively divides

Number Theory Level 4

If $N$ is divisible by $1,2,3,\ldots, 13$ , then $N$ must also be divisible by 14 and 15.

Using this same idea, what is the smallest integer $M$ such that the following statement is true?

If $N$ is divisible by $1,2,3,\ldots,M$ , then $N$ must also be divisible by $M+1,M+2,M+3,$ and $M+4$ .