Period of |sin 2x | + |cos 8x| is

Clearly period of $|\sin 2x |=\frac{π}{2}$ and period of $|\cos 8x|=\frac{π}{8}$

Now L.C.M. $\left(\frac{π}{8},\frac{π}{2}\right)=\frac{π}{2}$ ⇒ Period of the given function is $\frac{π}{2}$