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Three bells ring simultaneously at 7 p.m. They ring at regular intervals of 15 minutes, 18 minutes and 20 minutes respectively. The time when all the three bells will ring together is:

Three bells ring simultaneously at 7 p.m. They ring at regular intervals of 15 minutes, 18 minutes and 20 minutes respectively. The time when all the three bells will ring together is: Correct Answer 10 p.m.

Given:

Three bells ring simultaneously at 7 p.m.

They ring at regular intervals of 15 minutes, 18 minutes and 20 minutes respectively. 

Concept used:

The concept of Lowest common multiple (LCM) will be used

Calculations:

According to the question, we have

All bells ring at regular intervals of 15 minutes, 18 minutes and 20 minutes respectively

LCM of 15, 18 and 20 is 

⇒ 15 = 3 × 5

⇒ 18 = 2 × 3 × 3

⇒ 20 = 2 × 2 × 5

⇒ LCM = 2 × 2 × 3 × 3 × 5

⇒ LCM = 180

All bells ring after 180 minutes

As we know, 60 Minutes = 1 hour

So, 180 minutes = 3 hours 

Thus, all bells ring after 3 hours 

⇒ 7 p.m. + 3 hours

⇒ 10 p.m.

∴ All the three bells ring after 10 p.m.

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