Given a finite summation of sines and cosines of the form $$\sum\limits_{i=1}^{n} \left(A_i\sin(\omega_ix)\right)+\sum_{j=1}^p \left(B_j\cos(\sigma_jx)\right)$$ where $A_i,\omega_i\in\mathbb{Z}$ $\forall i\in[1,n]\cap\mathbb{N}$ and $B_j,\sigma_j\in\mathbb{Z}$ $\forall j\in[1,p]\cap\mathbb{N}$. How do we prove that the least period of the summation is the LCM of the periods of the constituent sines and cosines?
The challenge I am having is in proving that the LCM of individual periods is in fact the smallest period of the resulting periodic summation.