Question
Download Solution PDFTwo alarm clocks ring their alarms at regular intervals of 90 seconds and 44 seconds. If they first beep together at 6:00 pm, at what time will they beep together for the next time?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Alarm 1 interval = 90 seconds
Alarm 2 interval = 44 seconds
First beep together at 6:00 PM
Formula Used:
Time for next beep together = LCM (Least Common Multiple) of the intervals
Calculation:
LCM of 90 and 44:
Prime factorization of 90 = 2 × 32 × 5
Prime factorization of 44 = 22 × 11
LCM = Product of the highest powers of all prime factors
LCM = 22 × 32 × 5 × 11 = 1980 seconds
1980 ÷ 60 = 33 minutes and 0 seconds
Next beep together = 6:00 PM + 33 minutes
⇒ Next beep together = 6:33 PM
∴ The correct answer is option 4.
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