The period of the sum of two periodic functions is at most the lowest common multiple of the periods of the two functions that make up the sum.
Determining the actual period is trickier. I am looking at a specific example: $$f(x)=|\text{cos}(x)|+|\text{sin}(x)|$$
$|\text{cos}(x)|$ and $|\text{sin}(x)|$ each have period $\pi$. But, $f(x)$ has period $\frac{\pi}{2}$, which is exactly half of the individual periods.
I understand how to get the period if I look at the graph on geogebra, or were to perhaps draw the graph myself.
But what features of the two functions result in this property? Is dividing something that occurs elsewhere also? And is it always 2, or some other number as well?
