How to find period of a sum of periodic functions

Question

I got this function:

$$ x[n]=\sin(2*\pi*4/3*n) + \cos(2*\pi*5/2*n) $$

It is easy to see that period of the sin is 3/4 and the period of the cos is 2/5.

Now, what do I have to do to get the period of the whole function?

I know that the period is 6. Solved in this wolfram alpha result.

Thanks in advance.

Answer 1

If two periodic functions $f(x)$ and $g(x)$ have periods $T_{1}$ and $T_{2}$ respectively. The sum $f(x)+g(x)$ has period $lcm(T_{1},T_{2})$.

In this case, the lowest common multiple (that is an integer) of $\frac{3}{4}$ and $\frac{2}{5}$ is 6.