SOLUTION: In the mathematics department of a college there are 60 first year student, 84 second year students, and 108 third year students .All these students are to be divided into project

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Question 1083329: In the mathematics department of a college there are 60 first year student, 84 second year students, and 108 third year students .All these students are to be divided into project groups such that each group has the same no of first year student, the same no of second year student, and the same no of third year students. What is the smallest possible size of each group?
a)19 b)9 c)12 d)21
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
it looks like 12 groups would do the trick.

each group will have 5 first year students and 7 second year students and 9 third year students.

19 groups won't do it because 60/19 is not an integer.

9 groups won't do it because 60/9 is not an integer.

21 groups won't do it because 60/21 is not an integer.

the only number of groups that leads to integers is 12.

60/12 = 5
84/12 = 7
108/12= 9

you will have 12 groups, with each group containing 5 first year students, 7 second year students, and 9 third year students.

that has to be it.