Finding the period of complex exponential function

Question

I am having some trouble finding the period of the following discrete signal:

$x[n]=e^{jn2\pi/3}+e^{jn3\pi/4}$

Answer 1

It is a composition of two complex exponentials each with it's own fundamental frequency. $$e^{j2\pi f_0n}$$ This way the exponentials would have frequencies $$f_1 = \frac{1}{3}$$ $$f_2 = \frac{3}{8}$$ And because neither of both frequencies can be simplified anymore then the fundamental period is defined to be the denominator of the expressions above so $$ T_1 = 3 $$ $$ T_2 = 8 $$

Answer 2

To sum up, our singal is periodic (because it is a superposition of two periodic signals) and it's primitive period is equal to the Least Common Multiple of the periods of the two composing signals. In this case LCM{3,8} = 24.

So the (primitive) period of the above-mentioned signal is T = 24.