Sine Curve Simultaneous equation help

Hello everyone, this is my first post, be kind =).

I have three sin curves, for 'biorhytms' (those lame scenarios they gives us for math assignments) each with a different period the equations are as follows;

y=sin(2pi/33*x)

y=sin(2pi/23*x)

y=sin(2pi/28*x)

where x is the number of days after birth. What I'm trying to find is the day in which all three curves equal zero, after x=0 of coruse. I get down to a whole number integar of the period on two for each one. And realised it must be a common multiple of all three, but how best do you show this? Thank you! Any help is much appreciated!