Answer:
90 seconds will pass before the gears are in line again
Step-by-step explanation:
In a clock, a large gear completes a rotation every 45 seconds.
The small gear completes a rotation every 18 seconds.
To get the number of seconds needed so these both will pass before the gears are in line again, we will simply find the LCM of 45 and 18.
45 = 3 x 3 x 5
18 = 2 x 3 x 3
LCM = 2 x 3 x 3 x 5 = 90
Hence, 90 seconds will pass before the gears are in line again