Question
Download Solution PDFThree bells make a beeping sound after every 48 seconds, 72 seconds 108 seconds respectively. They beeped together at 10 AM. The time (hh:mm:ss), when they will next beep together at the earliest is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Bells beep every 48 seconds, 72 seconds, and 108 seconds respectively.
They beeped together at 10 AM.
Formula Used:
Time when they will beep together again = LCM(48, 72, 108)
Calculation:
Prime factorization of 48: 24 × 3
Prime factorization of 72: 23 × 32
Prime factorization of 108: 22 × 33
LCM = 24 × 33
LCM = 16 × 27
LCM = 432 seconds
432 seconds = 432 / 60 = 7 minutes 12 seconds
10:00:00 + 00:07:12 = 10:07:12
The time when they will next beep together at the earliest is 10:07:12.
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