An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10…

Question

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

1. A. 10.30 a.m
2. B. 10.31 a.m (Correct answer)
3. C. 10.59 a.m
4. D. 11 a.m

Correct Answer

Option B — 10.31 a.m

Detailed Solution & Explanation

The correct answer is 10.31 a.m.

Key Points

• The devices beep together again after a time equal to the LCM of 60 and 62 seconds.
• 60 = 2² × 3 × 5 and 62 = 2 × 31, so LCM = 2² × 3 × 5 × 31 = 1860 seconds.
• 1860 seconds = 31 minutes.
• Starting from 10:00 a.m., they next beep together at 10:31 a.m.

Additional Information

• The rule of thumb for these problems: use the LCM when asking *when events coincide again*, and the HCF when asking for the *largest common measure* (cutting equal pieces, largest identical groups).
• If the two intervals are co-prime, the LCM is simply their product — a useful shortcut when no common factor exists.
• Note the wording trap: the question asks for the next beep together, so the answer is start time plus one LCM, not a multiple of it.