Fourier series - addition of cosine and sine of different frequencies

I need to find the Fouier series of the following:

f(t) = cos(4t) + sin(6t)

I know what they are individually, but for both of them added together I get a period of (pi / 2) / (pi / 3) = 3 / 2 so the period is 6,,, correct? The fourier series by themselves are just cos(4t) and sin(6t) repectively. Do you just place this expression in the formulae with T = 6? That's a lot of messy math. Any help on how to do this would be very much appreciated.

In addition, when I graph this on Matlab the period is smaller than 6. It looks a little bigger then 3. Any hints on what's going on?

Thanks