What is the fundamental period of cos(4t) + sin(6t)?

Question

What is the fundamental period of $\cos(4t) + \sin(6t)$?

How to find it? I tried doing it by using $T_1M_1=T_2M_2$ and got $12$ but my textbook is saying it it $\pi$.

Answer 1

The fundamental period is the l.c.m. (in $\mathbf Q\pi$) of the fundamental periods of the terms, $\dfrac{2\pi}4$ and $\dfrac{2\pi}6$, i. e. $$\pi\operatorname{lcm}\Bigl(\frac12,\frac13\Bigr)=\pi\frac1{\gcd(2,3)}=\pi. $$