A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM.
The immediate next time that they will beep together is \(\underline{\hspace{2cm}}\)
The immediate next time that they will beep together is \(\underline{\hspace{2cm}}\)
Show Hint
- 10:08 AM
- 10:42 AM
- 11:00 AM
- 10:00 PM
The Correct Option is A
Solution and Explanation
To find the next time both watches beep together, we need to calculate the least common multiple (LCM) of the two times, 30 seconds and 32 seconds. The LCM of 30 and 32 is calculated as follows: \[ \text{LCM}(30, 32) = 2^5 \times 3 \times 5 = 480 \text{ seconds}. \] This means that both watches will beep together again after 480 seconds. Now, converting 480 seconds to minutes: \[ 480 \text{ seconds} = 8 \text{ minutes}. \] So, they will beep together again 8 minutes after 10:00 AM, which is 10:08 AM.
Final Answer: (A)
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