In a seminar, the number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. 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?

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Detailed Solution

Given participants are,
Hindi = 60,
English = 84 and
Mathematics = 108
Here, the highest common factor, HCF of 60, 84, and 108 has to be find for the number of participants seated in room.
First, we shall factories 60, 84, and 108 as,

60 = 2^{2} \times 3 \times 5,

84 = 2^{2} \times 3 \times 7

and

108 = 2^{2} \times 3^{3}

As,

2^{2} \times 3

is common in each factor. So, HCF of 60,84 and 108 is

2^{2} \times 3 = 12

.
Therefore, in each room 12 participants can be seated.
The overall number of students will now be determined.
= 60+84+108
=252
So, number of rooms required,