Question

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?

Answer 1

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