Four gears are in constant mesh with each other. Gear A meshes only with Gear B, B meshes with A and C, C meshes with B and D, and D meshes only with C, like this:

A B C D

Gears A, B, C, and D have 35, 27, 84, and 34 teeth, respectively.

If a vertical stripe is painted on each gear, what is the minimum number of revolutions (>0) gear A would have to make before the four stripes are vertical again?

Though the answer works out to the same, it should be noted that the lines on gears C and D would be vertical even after only half a revolution, so the total number of teeth to advance would be calculated as the LCM of 35, 27, 42 and 17.