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Six bells ring at intervals of 2, 3, 5, 6, 9, 12 minutes respectively. They started ringing simultaneously at 5.00 am. Until 2.00 pm, how many times all the bells will ring together?
  • a)
    4 times  
  • b)
    2 times  
  • c)
    6 times  
  • d)
    3 times 
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Six bells ring at intervals of 2, 3, 5, 6, 9, 12 minutes respectively....

LCM = 2 x 3 x 5 x 3 x 2
= 180 minutes or 3 hours.
Time interval between 5.00 am to 2.00 pm = 9 hours.  
So, for 9 hours, they will ring for 9/3 = 3 times
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Most Upvoted Answer
Six bells ring at intervals of 2, 3, 5, 6, 9, 12 minutes respectively....

Analysis:
To find out how many times all the bells will ring together, we need to find the least common multiple (LCM) of the time intervals at which each bell rings.

Calculating LCM:
- The LCM of 2, 3, 5, 6, 9, and 12 is 180 minutes.
- Therefore, all the bells will ring together every 180 minutes.

Calculating Total Number of Times:
- From 5.00 am to 2.00 pm is a total of 9 hours, which is 540 minutes.
- Dividing 540 by 180, we get 3.
- This means that all the bells will ring together 3 times during this period.

Therefore, the correct answer is option D - 3 times.
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Six bells ring at intervals of 2, 3, 5, 6, 9, 12 minutes respectively. They started ringing simultaneously at 5.00 am. Until 2.00 pm, how many times all the bells will ring together?a)4 times b)2 times c)6 times d)3 timesCorrect answer is option 'D'. Can you explain this answer?
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