# 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? - Mathematics

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?

#### Solution

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 =  1860/60 = 31min
Hence, they will beep together again at 10 : 31 a.m.

Concept: Euclid’s Division Lemma
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