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wariber [46]
3 years ago
14

Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively. How many times will t

hey ring together at the same second in one hour excluding the one at the end?
Mathematics
1 answer:
Evgen [1.6K]3 years ago
6 0

Answer:

60 times will they ring together at the same second in one hour excluding the one at the end.

Step-by-step explanation:

Given : Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively.

To find : How many times will they ring together at the same second in one hour excluding the one at the end?

Solution :

First we find the LCM of 3, 6, 10, 12 and 15.

2 | 3  6  10  12  15

2 | 3  3   5   6  15

3 | 3  3   5   3  15

5 | 1    1  5   1    5

  | 1    1   1   1     1

LCM(3, 6, 10, 12,15)=2\times 2\times 3\times 5

LCM(3, 6, 10, 12,15)=60

So, the bells will ring together after every 60 seconds i.e. 1 minutes.

i.e. in 1 minute they rand together 1 time.

We know, 1 hour = 60 minutes

So, in 60 minute they rang together 60 times.

Therefore, 60 times will they ring together at the same second in one hour excluding the one at the end.

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