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There are three bells which ring at regular intervals of 30, 45 and 60 seconds respectively. If all of them ring together at 1:00 PM, at what time will they ring together again?

There are three bells which ring at regular intervals of 30, 45 and 60 seconds respectively. If all of them ring together at 1:00 PM, at what time will they ring together again? Correct Answer 1:03 PM

Given:

Three bells ring at regular intervals of 30, 45 and 60 seconds respectively

All of them ring together at 1:00 PM

Concept:

Find LCM of 30, 45, and 60 

Calculation:

LCM (30, 45, 60) = 180

To find LCM, use Prime factorisation method: Factorise the numbers into prime numbers and multiply all the prime numbers with the highest power

Here,

30 = 5 × 3 × 2 

45 = 5 × 3 × 3 = 5 × 32

60 = 5 × 3 × 2 × 2 = 5 × 3 × 22

So, LCM = 5 × 32 × 22 = 180

⇒ After 180 Seconds (ie; 3 Minutes) they will ring together again

∴ They will ring together again at 1:03 PM

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