From a point $P$, on the surface of radius 3 cm, two cockroaches $A$ and $B$ started moving along two different circular paths, each having the maximum possible radius, on the surface of the sphere, that lie in the two different planes which are inclined at an angle of 45 degree to each other. If $A$ and $B$ takes 18 sec and 6 sec respectively, to complete one revolution along their respective circular paths, then after how much time will they meet again, after they start from $P$?
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