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 numbers of participants are to be seated and all of them being in the same subject.

The number of room will be minimum if each room accommodates maximum number of participants.

∵ 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

So HCF of 60, 84 and 108 -

Prime factors of numbers are -

60 = 2 × 2 × 3 × 5

84 = 2 × 2 × 3 × 7

108 = 2 × 2 × 3 × 3 × 3

∴ HCF = 2 × 2 × 3 = 12

Therefore, in each room 12 participants can be seated.

Total number of students = 60 + 84 + 108 = 252

So minimum number of room required to accommodate all students = 252/12 = 21