Statement -I Period of ${\cos }^{3}x+{\cos }^3\left({120}^0-x\right)+{\cos }^3\left({120}^0+x\right)\text{ is }\frac{\pi }{3}$.

Statement -II Period of $2\cos \frac{\pi x}{3}+\sin \frac{\pi x}{2}-\tan \frac{\pi x}{4}\text{ is }12$

Which of the above statements is correct?

$$\begin{gathered} {\cos }^{3}x+{\cos }^3\left({120}^0-x\right)+{\cos }^3\left({120}^0+x\right)=\frac{1}{4}\cos 3x \\ period=\frac{2\mathrm{\pi }}{3} \end{gathered}$$

$$\begin{gathered} period of \cos \frac{\mathrm{\pi }}{3}x =\frac{2\mathrm{\pi }}{{\displaystyle \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=6 \\ period of \sin \frac{\pi x}{2}=\frac{2\mathrm{\pi }}{{\displaystyle \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}=4 \\ period of\tan \frac{\pi x}{4}=\frac{\mathrm{\pi }}{{\displaystyle \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}=4 \\ period of f\left(x\right)=2\cos \frac{\pi x}{3}+\sin \frac{\pi x}{2}-\tan \frac{\pi x}{4}= LCM 0f \left\{4,6\right\}=12 \end{gathered}$$