Consecutively divides

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 \(M+4\).

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