Question

Four bell rings simultaneously and afterwards at interval of 3 6 9 and 12 second respectively how often will they all ring together in one hour ?

Answer 1

Answer:

100 times

Step-by-step explanation:

Now assume you have 4 bells

• The 3 second bell rings every 3 seconds. so do the 6,9 and the 12 second bells
• now the largest time consuming bell is the 12 second one
• so the 3 and 6 sec bell shall ring along with the 12 sec bell, but the 9 second bell doesn't.
• So here the concept of LCM is applied
• By finding the lowest common factor, we can say when the 2 bells coincide.
• the lowest common factor of 3,6,9 and 12 is 36
• So every 36 sec the bells ringing coincides
• To explain further, During the 36th second

1. The 3 sec bell will ring for the 12th time
2. The 6 sec bell shall ring for the 6th time
3. the 9second bell shall ring for the 4th time
4. the 12 second bell shall ring for the 4th time

Taking all of this into consideration,

we are saying that it takes 36 seconds for all the bells to ring at once

Now In an hour there are 60 minutes

And in every minute there is 60 seconds

So in an hour there are 3600 seconds

To find no of times the bells ring simultaneously we have to

3600/36= 100

So there you go

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Answer 2

Answer:

6=2×3

7=1×7

8=2×2×2

9=1×3×3

select d max count for 2,3,7 for 2. Its in 8 = 2×2×2.

for 3 . Its in 9 = 3×3

Then 7 only once in any combination

L.C.M= 2×2×2×3×3×7= 8×9×7

L.C.M = 504

So all the bells ring together after 504 seconds

I hope this ans is help u