Question

seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.

Jagranjosh

1. In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are

a) 14

b) 12

c) 16

d) 18

Answer 1

Given : A seminar is being conducted by an educational organization, where the participants will be educators of different subjects. The number of participants in Hindi, English & Mathematics are 60, 84 & 108 respectively​

To Find :  In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are

Additional :

Total Number of participants

LCM

108 as product of primes

Solution:

Hindi = 60

English = 84

Maths = 108

Total = 60 + 84 + 108    = 252

60  = 2  x 2  x  3  x 5

84  = 2  x 2  x  3  x 7

108  = 2 x  2 x  3 x  3 x 3

HCF  = 2 x  2 x  3  =  12

maximum number participants that can accommodated in each room  = 12

LCM =  2 x  2 x  3 x  3 x 3 x 5 x 7

= 3780

108  = 2 x  2 x  3 x  3 x 3

=> 108 = 2² x 3³

maximum number participants that can accommodated in each room are 12

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Answer 2

$\huge\pink{\mathbb{Hello}}..$

Since the least numbers of a room are required.

So, number of participants in each room must be the H.C.F. of 60, 84, and 108.

$60 = {2}^{2} \times 3 \times 5$

$84 = {2}^{2} \times 3 \times 7$

And

$108 = {2}^{2} \times {3}^{3}$

HCF of 60, 84 and 108.

$= {2}^{2} \times 3 = 4 \times 3 = 12$

Therefore, in each room 12 participants can be seated.

Number of rooms required

$= \frac{total \: no.of \: participant}{12}$

$= \frac{60 + 84 + 108}{12}$

$= \frac{252}{12} = 21$

✈︎✈︎✈︎Hence, required no .of rooms= 12