Question

In a seminar number of participants in Hindi , English and Mathematics are $60,84$ and $108$ respectively. If the equal number of participants of the same subject are sitting in each room, then find the least number of required rooms.

Answer 1

Since the least numbers of a room are required.
So, number of participants in each room must be the H.C.F of $60,84$ and $108$.
$60=2^2\times 3\times 5$
$84=2^2\times 3\times 7$
and $108=2^2\times 3^3$
HCF of $60,84$ and $108=2^2\times 3=4\times 3=12$.

Therefore, in each room $12$ participants can be seated.

$\therefore$ Number of rooms required $=\frac{Totalnumberofparticipants}{H.C.F}$

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

Hence $21$ room are needed.