One gear turns 33 1/3 times in a minute. Another gear turns 45 times in a minute. Initially, a mark on each gear is pointing due north. After how many seconds will the two gears next have both their marks pointing due north?
The answer is not 15.
First gear will make =60 / 33 1/3 =9/5 turns per second.
Second gear will make =60 / 45 =4/3 turns per second.
LCM[9/5, 4/3] = 36 seconds - when both their marks will be pointing due north.