Question

The Ancient Wizard Albus owns 3 ancient Clocks of Perpetual Motion. Every day, Clock #1 runs 20 minutes fast; Clock #2 runs 30 minutes fast, and Clock #3 runs 40 minutes fast. He sets all three clocks to the correct time and leaves to visit his friend. After many days, he returns home and, to his surprise, finds all 3 clocks showing the correct time again! What is the fewest possible number of days Albus could have spent away from home?

Answer 1

Answer:

the fewest possible number of days is 72

Answer 2

Answer:

72 days

Step-by-step explanation:

After they are 12 hours off, it will show the correct time.

12 hours in minutes would be 12*60=720 minutes

720 / 20 = 36 days for the first clock to return to the correct time

720 / 30 = 24 days for the second clock to return to the correct time

720 / 40 = 18 days for the third clock to return to the correct time

To get the day all the clocks show the correct time, we need the lcm

lcm(36,24,18) = 72 days.