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Three clocks are designed to alarm in every hour, two hours and three hours respectively. If they all alarmed together three hours before, then after how many hours from now will they next alarm together? A. 3 hours B. 6 hours C. 2 hours D. 1 hours

Three clocks are designed to alarm in every hour, two hours and three hours respectively. If they all alarmed together three hours before, then after how many hours from now will they next alarm together? A. 3 hours B. 6 hours C. 2 hours D. 1 hours Correct Answer A

LCM of 1 hour, 2 hours, and 3 hours = 6 hours

∴ All the clock's alarm together at an interval of 6 hours.

They all alarmed together three hours before.

∴ They will again alarm together after 3 hours

Detailed solution:

Given:

Three clocks are designed to alarm every hour, two hours, and three hours respectively.

They all alarmed together three hours before:  

Calculation:

3 Clocks are designed to alarm every 1, 2 and, 3 hour

Such that clock A will alarm every hour, B will alarm once in 2 hours, C will alarm once in 3 hours.

Starting from 12 pm,

A alarm = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

B alarm = 2, 4, 6, 8, 10, 12

C alarm = 3, 6, 9, 12

Common alarm at 6, 12

They all alarmed together three hours before.

∴ The common alarm will be 3 hours later.

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