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

Step-by-Step Solution1. Identify the intervals:Device 1 beeps every 60 seconds.Device 2 beeps every 62 seconds.2. Find the LCM of 60 and 62:To find the next time they beep together, we calculate $LCM(60, 62)$.Prime factorization of 60: $2^2 \times 3 \times 5$Prime factorization of 62: $2 \times 31$$LCM = 2^2 \times 3 \times 5 \times 31 = 1860$ seconds.3. Convert seconds into minutes:Since the answer needs to be in a time format, we convert 1860 seconds into minutes:$$\frac{1860}{60} = 31 \text{ minutes}$$4. Calculate the next time:They first beeped together at 10:00 a.m.Adding 31 minutes to 10:00 a.m. gives us 10:31 a.m.