Answer:
They will next toll together at 8:00 pm
Step-by-step explanation:
To find after how many minutes they will toll together next, we have to find the least common multiple of their frequencies.
The frequencies are of: 15 minutes, 16 minutes and 36 minutes.
Finding the least common multiple, by factoring all of the numbers by prime factors:
15 - 16 - 32|2
15 - 8 - 16|2
15 - 4 - 8|2
15 - 2 - 4|2
15 - 1 - 2|2
15 - 1 - 1|3
5 - 1 - 1|5
1 - 1 - 1
The last common multiple between 15, 16 and 36 is of: [tex]2^5*15 = 32*15 = 480[/tex]
480 minutes is 480/60 = 6 hours, so they will next toll together 6 hours from 2:00 pm, that is, at 8:00 pm.
