OK,, I've been taught, maybe the wrong way, that in order to find a common period of two sums such as cos(4t) + sin(6t) you do the following:

Find periods: 2pi / 4 = pi / 2 -- This is first period T1

Next,, 2pi / 6 = pi / 3 -- This is second period T2

Now T1 / T2 must be rational so (pi / 2) * (3 / pi) = 3 / 2 which is rational. Now find LCM(3, 2) which is 6.

What is wrong with this? Why would a graph show it is pi which is an irrational number?