Lets say you have a set of functions F so that function f1 has a period p1 and so on. How would I go about to find the time t such that all the functions in F are at the start of a new period at t?
Example:
F = {sin(x), sin(2x), sin(0.5x)}
f1 intersects (as multiples of pi): [0, 1, 2, 3, 4]
f2 intersects (as multiples of pi): [0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4]
f3 intersects (as multiples of pi): [0, 2, 4]
The only common intersects are 0 and 4 so the period is 4
My initial thought was to take the LCM of the periods, however if the period is a real value I don't really know how to find the LCM.
Any suggestion for how to solve this without produce a set of all the indices that correspond to the start of a period and grabbing the intersection?
First, note that the periods line up if and only if they are rational multiples of one another. If this condition is satisfied, for example if the periods are $\alpha q_1,\dots,\alpha q_n$ for $\alpha \in \mathbb{R}$ and $q_1,\dots,q_n \in \mathbb{Q}$, then they all line up at time $$ \alpha \cdot\text{lcm}(q_1,\dots,q_n)$$ where the LCM of rational numbers are taken as in the comment above.