Question

in a seminar the no. of participants in hindi , english and mathematics are 60 , 84 and 108 find the minimum number. of rooms required it in each room ​

Answer 1

The Number of room will be minimum if each room accomodates maximum

number of participants. Since 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. The prime factorisations of 60,84 and 108 are as under.

60=2

2

×3×5,84=2

2

×3×7 and 108=2

2

×3

3

∴ HCF of 60,84 and 108 is 2

2

×3=12

Therefore, in each room 12 participants can be seated.

∴ Number of rooms required=

12

Total number of participants

=

12

60+84+108

=

12

252

=21