(D) The period of $\sin \frac{\pi x}{2}$ is $T_1 = \frac{2\pi}{\pi/2} = 4$.The period of $\cos \frac{\pi x}{3}$ is $T_2 = \frac{2\pi}{\pi/3} = 6$.The

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(D) The period of $\sin \frac{\pi x}{2}$ is $T_1 = \frac{2\pi}{\pi/2} = 4$.The period of $\cos \frac{\pi x}{3}$ is $T_2 = \frac{2\pi}{\pi/3} = 6$.The period of $\tan \frac{\pi x}{4}$ is $T_3 = \frac{\pi}{\pi/4} = 4$.The period of the function $f(x)$ is the $L.C.M.$ of $(T_1, T_2, T_3) = L.C.M.(4, 6, 4) = 12$.