SOLUTION: Four bells ring at intervals of 3,7,12 and 14minutes respectively.All four rang together at 12 noon.When will they ring together again?

Question 617343: Four bells ring at intervals of 3,7,12 and 14minutes respectively.All four rang together at 12 noon.When will they ring together again?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the answer, we need to find the LCM of 3, 7, 12, 14.

First, list the prime factorization of each number. If you need help with prime factorization, check out this solver.

3: 3

7: 7

12: 2*2*3

14: 2*7

Now highlight the unique factors. Remember, highlight the factors that occur most frequently

3: 3

7: 7

12: 2*2*3

14: 2*7

Now multiply all of the highlighted factors

2*2*3*7=84

So the LCM of 3, 7, 12, and 14 is 84

This means that every 84 minutes, the four bells will ring at the same time (you start the timer when they first ring)

So because 84 min = 60 min + 24 min = 1 hr 24 min, add this to 12:00 to get

12:00
 1:24
------
13:24

Since 13:24 is the same as 1:24 pm, this means that the four bells will ring together again at 1:24 pm
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