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Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time?
Most Upvoted Answer
Two alarm clocks ring their alarms at regular intervals of 50 seconds ...
Introduction:
In this problem, we need to find the time at which two alarm clocks will first ring together after they initially ring together at 12 noon. The alarm clocks have regular intervals of 50 seconds and 48 seconds respectively.
Approach:
To solve this problem, we need to find the least common multiple (LCM) of the intervals of the two alarm clocks. The LCM will give us the time at which both alarm clocks will ring together again.
Calculating the LCM:
To find the LCM of 50 seconds and 48 seconds, we can use the following steps:
1. Identify the prime factors of each number:
- The prime factors of 50 are 2 and 5.
- The prime factors of 48 are 2, 2, 2, and 2.
2. Take the highest power of each prime factor:
- The highest power of 2 is 2^4.
- The highest power of 5 is 5^1.
3. Multiply the highest powers of all prime factors:
- LCM = 2^4 * 5^1 = 80 * 5 = 400.
Therefore, the LCM of 50 seconds and 48 seconds is 400 seconds.
Calculating the time:
Since the two alarm clocks initially ring together at 12 noon, we need to add 400 seconds to this time to find the time at which they will ring together again.
1. Convert 400 seconds to minutes and seconds:
- 400 seconds = 6 minutes and 40 seconds.
2. Add the calculated time to 12 noon:
- 12 noon + 6 minutes + 40 seconds = 12:06:40 PM.
Conclusion:
The two alarm clocks will ring together again for the first time at 12:06:40 PM.
In this problem, we need to find the time at which two alarm clocks will first ring together after they initially ring together at 12 noon. The alarm clocks have regular intervals of 50 seconds and 48 seconds respectively.
Approach:
To solve this problem, we need to find the least common multiple (LCM) of the intervals of the two alarm clocks. The LCM will give us the time at which both alarm clocks will ring together again.
Calculating the LCM:
To find the LCM of 50 seconds and 48 seconds, we can use the following steps:
1. Identify the prime factors of each number:
- The prime factors of 50 are 2 and 5.
- The prime factors of 48 are 2, 2, 2, and 2.
2. Take the highest power of each prime factor:
- The highest power of 2 is 2^4.
- The highest power of 5 is 5^1.
3. Multiply the highest powers of all prime factors:
- LCM = 2^4 * 5^1 = 80 * 5 = 400.
Therefore, the LCM of 50 seconds and 48 seconds is 400 seconds.
Calculating the time:
Since the two alarm clocks initially ring together at 12 noon, we need to add 400 seconds to this time to find the time at which they will ring together again.
1. Convert 400 seconds to minutes and seconds:
- 400 seconds = 6 minutes and 40 seconds.
2. Add the calculated time to 12 noon:
- 12 noon + 6 minutes + 40 seconds = 12:06:40 PM.
Conclusion:
The two alarm clocks will ring together again for the first time at 12:06:40 PM.
Community Answer
Two alarm clocks ring their alarms at regular intervals of 50 seconds ...
LCM(50,48)=1200 seconds =20 minutesHence they will beep again for the first time at 12:20pm.
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Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time?
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Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time?.
Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds.If they first beep together at 12 noon,at what time will they beep again for the first time?.
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