# In a seminar, the number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. If in each room the same number of participants of the same subject are seated then find the minimum number of rooms required.

Given:

Number of participants for Hindi = 60

Number of participants for English = 84

Number of participants for Mathematics = 108

Number of participants for each room will be the HCF of 60, 84 and 108.

60 = 2 × 2 × 3 × 5

84 = 2 × 2 × 3 × 7

108 = 2 × 2 × 3 × 3 × 3

So for finding the HCF we may write as follows:

So HCF = 22 × 3

= 12

So total number of participants = 60 + 54 + 108

= 252

Number of rooms required = 252 / 12

= 21

So total 21 rooms are required.

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