in a delegation of students there are 60 indian,84 chinese and 108 british.they all want to stay in the same hotel.The no of students stay in each room is same and also will stay with their own country students.Find the minimum no. of rooms reqd. for stay of these students.Depict values.

To find the minimum no. rooms we first find the same no. students stay in each room throught H.C.F.
Take 60 and 84 
84 > 60
Apply Euclid's division Algorithm 
84 = 60 * 1 + 24
60 = 24 *2+12
24 = 12 *2 + 0
So here 12 is the h.cf. of 60 and 84 
now again take the remaining no. and appply lemma
108 = 12 * 9 + 0
So 12 is the h.c.f of 108, 84 , 60
No. of students in each room 12
NO. of rooms = 108/12 , 84 / 12 , 60 / 12
= 9 + 7 + 5
= 21  rooms 
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