$f\left(x\right)=max\{x/n,|\sin \pi x\left|\right\},n\in N$, has maximum points of non- differentiability for $x\in (0,4).$ Then $n$
cannot be 

$f\left(x\right)=max\left\{\frac{x}{n},|\sin \pi x|\right\}$

Thus, for the maximum points of non–differentiability, graphs of $y=\frac{x}{n}$ and $y=|\sin \pi x|$ must intersect at maximum number of points which occurs when $n > 3.5$.

Hence, the least value of n is 4.