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Three alarm clocks ring the alarm at 3, 6 and 9 minutes respectively. In 60 minutes how many times will the clocks ring together?
- a)3 times
- b)2 times
- c)4 times
- d)1 time
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Three alarm clocks ring the alarm at 3, 6 and 9 minutes respectively. ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27.....
Multiples of 6: 6, 12, 18, 24, 30.....
Multiples of 9: 9, 18, 27.....
The clocks ring in every 18 minutes together.
1st time the clock will ring in 18 minutes, then at 36 minutes and then at 54 minutes.
So in 60 minutes the clocks will ring 3 times.
Multiples of 6: 6, 12, 18, 24, 30.....
Multiples of 9: 9, 18, 27.....
The clocks ring in every 18 minutes together.
1st time the clock will ring in 18 minutes, then at 36 minutes and then at 54 minutes.
So in 60 minutes the clocks will ring 3 times.
Most Upvoted Answer
Three alarm clocks ring the alarm at 3, 6 and 9 minutes respectively. ...
Explanation:
To find out how many times the clocks will ring together we need to find the number of times they will meet at the same time. We can do this by finding the least common multiple (LCM) of 3, 6 and 9.
Finding the LCM:
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
- The multiples of 6 are: 6, 12, 18, 24, 30...
- The multiples of 9 are: 9, 18, 27, 36...
From the above multiples, we can see that the least common multiple of 3, 6 and 9 is 18. This means that the clocks will ring together every 18 minutes.
Calculating the number of times the clocks will ring together in 60 minutes:
To find out how many times the clocks will ring together in 60 minutes, we need to divide 60 by 18.
60 ÷ 18 = 3 remainder 6
This means that the clocks will ring together 3 times and will be left with 6 minutes. Therefore, the correct answer is option A, 3 times.
To find out how many times the clocks will ring together we need to find the number of times they will meet at the same time. We can do this by finding the least common multiple (LCM) of 3, 6 and 9.
Finding the LCM:
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
- The multiples of 6 are: 6, 12, 18, 24, 30...
- The multiples of 9 are: 9, 18, 27, 36...
From the above multiples, we can see that the least common multiple of 3, 6 and 9 is 18. This means that the clocks will ring together every 18 minutes.
Calculating the number of times the clocks will ring together in 60 minutes:
To find out how many times the clocks will ring together in 60 minutes, we need to divide 60 by 18.
60 ÷ 18 = 3 remainder 6
This means that the clocks will ring together 3 times and will be left with 6 minutes. Therefore, the correct answer is option A, 3 times.
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Community Answer
Three alarm clocks ring the alarm at 3, 6 and 9 minutes respectively. ...
Solution:
Therefore, the correct answer is option A, 3 times.
- The first alarm clock rings at 3 minutes, then at 6, then at 9, then at 12, and so on.
- The second alarm clock rings at 6 minutes, then at 12, then at 18, then at 24, and so on.
- The third alarm clock rings at 9 minutes, then at 18, then at 27, then at 36, and so on.
- The first time all three clocks will ring together is when they all ring at the 9th minute.
- The second time all three clocks will ring together is when they all ring at the 18th minute.
- The third time all three clocks will ring together is when they all ring at the 27th minute.
- The fourth time all three clocks will ring together is when they all ring at the 36th minute.
- Since the last time all three clocks will ring together is the 27th minute, they will only ring together 3 times in 60 minutes.
Therefore, the correct answer is option A, 3 times.
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Three alarm clocks ring the alarm at 3, 6 and 9 minutes respectively. In 60 minutes how many times will the clocks ring together?a)3 timesb)2 timesc)4 timesd)1 timeCorrect answer is option 'A'. Can you explain this answer?
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