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An electronic device makes a beep after every 45 seconds, another device makes a beep after every 60 seconds and the third device makes a beep after every 72 seconds. They beeped together at 8:30 am. At what time will they beep together at the earliest?

An electronic device makes a beep after every 45 seconds, another device makes a beep after every 60 seconds and the third device makes a beep after every 72 seconds. They beeped together at 8:30 am. At what time will they beep together at the earliest? Correct Answer 8:36 am

Given:

Time after which first device beeps = 45 sec.

Time after which second device beeps = 60 sec.

Time after which third device beeps = 72 sec.

Time when all devices beeped together = 8:30 am

Concept Used:

The time after which all the devices will beep together is LCM of the time of beep of individual devices.

Calculations:

Let the time after which all the devices will beep together be t.

Time of beep of first device = 45 sec.

Factors of 45 = 3 × 3 × 5

Time of beep of second device = 60 sec.

Factors of 60 = 2 × 2 × 3 × 5

Time of beep of third device = 72 sec.

Factors of 72 = 2 × 2 × 2 × 3 × 3

Time when all devices will beep together = t = LCM of (45, 60, 72) = 2 × 2 × 2 × 3 × 3 × 5 = 360 sec. = 360/60 mins = 6 mins

The time when all devices beep together earliest = 8:30 am + 6 mins = 8:36 am

∴ The time when all devices will beep together earliest is 8:36 am.

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