Question

In a seminar, the number of participants in Hindi, English and Mathematics are $60,84$ and $108$ respectively. Find the 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 participants in each room must be the $HCF$ of $60,84$ and $108$.

In order to find the $HCF$ of $60,84$ and $108$, we first the $HCF$ of $60$ and $84$ by Euclids division algorithm:
Clearly, $HCF$ of $60$ and $84$ is $12$.

Now, we find the $HCF$ of $12$ and $108$
Clearly, $HCF$ of $12$ and $108$ is $12$.
Hence, the $HCF$ of $60,84$ and $108$ is $12$.

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

Total number of participants $=60+84+108=252$
$\therefore$ Number of rooms required $=\frac{252}{12}=21$.