The student council and the dramatics club of a school share an auditorium for their practice. If both of them started on January 1, and the student council meets once every 3 days while the dramatics club meets once every 5 days, when will they share the auditorium again?
16 January
16 January is correct.
The two groups use the auditorium together again after a number of days that is a common multiple of 3 and 5, and the first such day comes after their LCM.
Since 3 and 5 have no common factor, their LCM is \(3 \times 5 = 15\) days.
Counting 15 days on from 1 January gives \(1 + 15 = 16\), so both meet in the auditorium again on 16 January.
Similar Questions
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Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
