In a seminar, the number of participants in Hindi, English and Mathematics are 60 , \textrm{ } 84 and 108 respectively. Find the number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

Foundation

Mathematics Foundation

HCF and LCM

Question

In a seminar, the number of participants in Hindi, English and Mathematics are

60, 84

and

108

respectively. Find the number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

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The number of participants in each room must be the

H C F

60, 84

and

108

In order to find the

H C F

60, 84

and

108

, we first the

H C F

60

and

84

by Euclids division algorithm:
Clearly,

H C F

60

and

84

12

Now, we find the

H C F

12

and

108

Clearly,

H C F

12

and

108

12

.
Hence, the

H C F

60, 84

and

108

12

Therefore, in each room maximum

12

participants can be seated.
Wehave,

Total number of participants

= 60 + 84 + 108 = 252

∴

Number of rooms required

= \frac{252}{12} = 21