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Question

Four bells rang at an interval of 3,7,12,14 mins respectively. All four bells rang at 12 noon . When will they ring together again

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Solution

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,

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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