Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

given that $\displaystyle x(t) = cos(600\pi t)$ and $\displaystyle m(t) = 4 + 3cos(20\pi t)$ what is the period (if any) of the resulting signal

Also the signal $\displaystyle x(t) = 10cos(600\pi t + \frac{\pi}{3}) + 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t) $ whats the period of the signal

Im not sure how to calculate the period when theres more than one sinusoid wave

Any help most appreciated