A clock shop has three cuckoo clocks on display. The cuckoos appear at different time intervals. One comes out every 10 minutes, one comes out every 15 minutes, and one comes out every 25 minutes. If they all appear at 5 o'clock, what is the next time they will all come out together?
The next time they will all come out together will be their least common multiple (LCM) of 10, 15, and 25 minutes.
First, let's find the LCM of 10 and 15.
- The multiples of 10 are: 10, 20, 30, 40, 50, ...
- The multiples of 15 are: 15, 30, 45, 60, 75, ...
The LCM of 10 and 15 is 30.
Now, let's find the LCM of 30 and 25.
- The multiples of 30 are: 30, 60, 90, 120, 150, ...
- The multiples of 25 are: 25, 50, 75, 100, 125, ...
The LCM of 30 and 25 is 150.
Therefore, the next time they will all come out together is 150 minutes after 5 o'clock, which is at 7:30.