Question

In a seminar, the number of participants in Hindi, English and Mathematics are $60,84$ and $108$ respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

Answer 1

The Number of room will be minimum if each room accomodates maximum

number of participants. Since in each room the same number of participants

are to be seated and all of them must be of the same subject. Therefore, the

number of participants in each room must be the $HCF$ of $60,84$ and

$108$. The prime factorisations of $60,84$ and $108$ are as under.

$60=2^2\times 3\times 5,84=2^2\times 3\times 7$ and $108=2^2\times 3^3$

$\therefore HCF$ of $60,84$ and $108$ is $2^2\times 3=12$
Therefore, in each room $12$ participants can be seated.

$\therefore Numberofroomsrequired=\frac{Totalnumberofparticipants}{12}$
$=\frac{60+84+108}{12}=\frac{252}{12}=21$