The angular frequencies are $ \frac3\pi7 $ and $ \frac4\pi7 $, so periods are $ \frac2\pi3\pi/7 = \frac143 $, and $ \frac2\pi4\pi/7 = \frac72 $. The LCM of $ \frac143 $ and $ \frac72 $ is found by expressing as rational multiples. - Groen Casting