Problem
In clock, a large gear completes a rotation every 45 seconds, and a small gear completes a rotation every 18 seconds. How many seconds pass before the gears align again?
Solution
For this case we can discompose the numbers on this way:
45= 9*5
18= 9*2
Let x the number of revolutions for the first case large gear and y for the second one small gear we want this:
x=y
9*5 *f1= 9*2 *f2
Where f1 and f2 represent the total time the final answer for this case is given by the LCM:
9*5*2 = 90 seconds
This value correspond to the LCM of 45 and 18
After 90 seconds we will have the gears align again