If I think of example like $\quad -sin[\pi n]+sin[\pi n] \;$
Although both functions have the same fundamental period 2, fundamental period of their sum is undefined. So how can I deal with the fundamental period of
$\; cos\left[\dfrac{7\pi n}{10}\right]+sin\left[\dfrac{13\pi n}{10}\right] \;$
They both have 20 as their fundamental period, but as I know from the first example that we cannot simply apply least common multiple rule. Are there any simple rules for solving these problems ?