The first clock becomes faster by 2 minutes every 12 hours, which means it gains 2 × 2=4 minutes per day.
The second clock becomes slower by 3 minutes every 12 hours, which means it loses 3 × 2=6 minutes per day.
For a 12 hour clock to show the correct time again, it must gain or lose a total of 12 hours.
The total minutes in 12 hours are 12 × 60=720 minutes
The first clock gains 4 minutes per day, so it will take 720/4=180 days to show the correct time again.
The second clock loses 6 minutes per day, so it will take720/6 =120 days to show the correct time again.
To find the minimum number of days after which both clocks will again show the correct time, the least common multiple (LCM) of the individual times must be found. The LCM of 180 and 120 is calculated.
LCM = 360
