An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 a.m. The next time, when they would beep together at the earliest is:

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  1. 10:30 a.m
  2. 10:31 a.m
  3. 10:59 a.m
  4. 11:00 a.m

Answer (Detailed Solution Below)

Option 2 : 10:31 a.m
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Detailed Solution

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Given:

An electronic device makes a beep after every 60 sec.

Another device makes a beep after every 62 sec.

They beeped together at 10 a.m.

Formula used:

The earliest time they will beep together is given by the Least Common Multiple (LCM) of their beep intervals.

LCM of 60 and 62

Calculation:

Prime factorization:

60 = 2 × 2 × 3 × 5

62 = 2 × 31

LCM = 22 × 3 × 5 × 31

LCM = 4 × 3 × 5 × 31

LCM = 60 × 31

LCM = 1860 sec

Convert 1860 seconds into minutes:

1860 sec ÷ 60 sec/min = 31 minutes

⇒ 10:00 a.m. + 31 minutes = 10:31 a.m.

∴ The correct answer is option 2.

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