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 is to be seated and all of them being in the same subject.

Answer 1

Dear Student
Minimum number of rooms required = $\frac{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{participants}}{\mathrm{HCF}(60,84,108)}$

Prime factorization of 60, 84 and 108 is:

60 = 2² × 3 × 5
84 = 2² × 3 × 7
108 = 2² × 3³

HCF = product of smallest power of each common prime factor in the numbers = 2² × 3 = 12

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

Therefore, minimum number of rooms required = $\frac{252}{12}=21$

Thus, minimum number of rooms required is 21.
Regards