Question

Find the period of $\sin 3x+\cos \pi x$

Answer 1

Period$=$LCM$\{\frac{2\pi }{3},2\}$

as LCM of irrational and rational not possible hence $f\left(x\right)$ is non periodic

($\frac{2\pi }{3}$ is irrational and $2$ is rational).