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5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 minutes, 4 minutes and 10 minutes, respectively. In 8 hours from the moment they start, how many times will they ring together?
- a)12 times
- b)5 times
- c)3 times
- d)4 times
- e)8 times
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 m...
We need the next instances when the alarm rings.
That means the Least Common Multiple (LCM) of 3, 4, 8, 10, 12 3, 4 divide 12 so neglect them.
LCM of 8, 10 and 12
∴ LCM = 4x2x5x3= 120 = They ring after 2 hours
After starting, they ring together ist time in 2 hours.
Then 2nd time in 2+2 = 4 hours.
Then 3rd time in 6 hours.
And 4th time in 8 hours.
That means the Least Common Multiple (LCM) of 3, 4, 8, 10, 12 3, 4 divide 12 so neglect them.
LCM of 8, 10 and 12
∴ LCM = 4x2x5x3= 120 = They ring after 2 hours
After starting, they ring together ist time in 2 hours.
Then 2nd time in 2+2 = 4 hours.
Then 3rd time in 6 hours.
And 4th time in 8 hours.
Most Upvoted Answer
5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 m...
Solution:
To solve the problem, we need to find the LCM (Least Common Multiple) of the given intervals, which is the time after which all the clocks will ring together for the first time. We can then count the number of times they will ring together in 8 hours or 480 minutes.
Finding LCM:
We can use the division method to find the LCM of the given intervals.
Step 1: Write the given intervals in a row.
12 8 3 4 10
Step 2: Divide the row by the smallest prime number that divides at least two of the numbers. Write the quotients and the remaining numbers in a new row below.
2 4 1 1 5
6 2 1 1
3 1 1
Step 3: Repeat step 2 until all the numbers in the row are prime.
2 2 3 2 5
1 1 1 1
1
Step 4: The LCM is the product of all the prime numbers and the remaining numbers with the highest power.
LCM = 2^2 x 3 x 5 x 1 x 1 = 60 minutes
Counting the number of times the clocks will ring together:
In 8 hours or 480 minutes, the clocks will ring together every 60 minutes. Therefore, they will ring together 8 x 60 / 60 = 8 times in 8 hours.
Therefore, the correct answer is option D, 4 times.
To solve the problem, we need to find the LCM (Least Common Multiple) of the given intervals, which is the time after which all the clocks will ring together for the first time. We can then count the number of times they will ring together in 8 hours or 480 minutes.
Finding LCM:
We can use the division method to find the LCM of the given intervals.
Step 1: Write the given intervals in a row.
12 8 3 4 10
Step 2: Divide the row by the smallest prime number that divides at least two of the numbers. Write the quotients and the remaining numbers in a new row below.
2 4 1 1 5
6 2 1 1
3 1 1
Step 3: Repeat step 2 until all the numbers in the row are prime.
2 2 3 2 5
1 1 1 1
1
Step 4: The LCM is the product of all the prime numbers and the remaining numbers with the highest power.
LCM = 2^2 x 3 x 5 x 1 x 1 = 60 minutes
Counting the number of times the clocks will ring together:
In 8 hours or 480 minutes, the clocks will ring together every 60 minutes. Therefore, they will ring together 8 x 60 / 60 = 8 times in 8 hours.
Therefore, the correct answer is option D, 4 times.
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5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 minutes, 4 minutes and 10 minutes, respectively. In 8 hours from the moment they start, how many times will they ring together?a)12 timesb)5 timesc)3 timesd)4 timese)8 timesCorrect answer is option 'D'. Can you explain this answer?
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