An electronic device makes a beep after every 60 seconds. Another device makes a beep after every 62 seconds. They beeped together at 10 a.m. At what time will they beep together at the earliest?
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Given:
Beep duration of first device = 60 seconds
Beep duration of second device = 62 seconds
To find the interval of beeping together, we need to find the LCM of 60 and 62 first.
60 = 2 x 2 × 3 × 5
62 = 2 × 31
LCM = 2 x 2 × 3 × 5 × 31 = 1860 seconds
Convert time into mins:
160 sec = 1860/60 mins = 31 min
Electronic devices will beep after every 31 minutes.
Hence, both devices will beep together again at 10:31 a.m. again.
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Beep duration of first device = 60 seconds
Beep duration of second device = 62 seconds
∴ Interval of beeping together = LCM (60, 62)
Prime factorization:
60 = 22 × 3 × 5
62 = 2 × 31
∴ LCM = 22 × 3 × 5 × 31 = 1860 seconds = \(\frac{1860}{60}\) = 31 min
Hence,
they will beep together again at 10 : 31 a.m.
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