Question

- 5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 minutes, 4 minutes and 10 minutes, respectively. In 8 hours from the moment they start, how many times will they ring together?

Answer 1

Given :-

• 5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 minutes, 4 minutes and 10 minutes, respectively.

To Find :-

• In 8 hours from the moment they start, how many times will they ring together ?

Concept Used :-

• Clock Run together for The first time after the time Equal to the LCM of All given Clocks Individual Time.

Solution :-

LCM of 12 , 8, 3 , 4 & 10 :-

→ 12 = 2 * 2 * 3 = 2² * 3

→ 8 = 2 * 2 * 2 = 2³

→ 3 = 1 * 3

→ 4 = 2 * 2 = 2²

→ 10 = 2 * 5

LCM = 3 * 2³ * 5 = 3 * 8 * 5 = 120 Minutes.

So,

→ The clock Rings Together for The first time after = 120 Minutes = 2 Hours.

Hence,

→ in 8 Hours clock Ring Together = 8/2 = 4 Times..(Ans.)

Therefore in 8 Hours from the moment they start ,they ring together for 4 Times.

Answer 2

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$\huge\tt{GIVEN:}$

• 5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 minutes, 4 minutes and 10 minutes, respectively.

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$\huge\tt{TO~FIND:}$

• In 8 hours from the moment they start, how many times will they ring together?

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$\huge\tt{SOLUTION:}$

Least Common Multiple or L.C.M of 12,18,3,4,10 is 120

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Then,

The clock would ring together after = 120 minutes or 2 Hours

Therefore,

Clocks would together ring in 8 hours = 8÷2 or 4 Times.

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In 8 hours, clocks would ring 4 Times...

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