Question

in a seminar , the number of participants for the events of drama , dance and music are 60,84and 108 respectively . find the minimum number of rooms required, if the number of participants to be seated in each room is the same and all of them being in the same group.​

Answer 1

$\huge\tt{\bold{\underline{\underline{Given᎓}}}}$

The number of participants for the events of drama , dance and music are 60,84and 108 respectively

To find :

The minimum number of rooms required.

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

Step by step explanation:

Note :if the number of participants to be seated in each room is the same then the number of room will be minimum.

Minimum number of rooms required =Total number of participants (60,84&108)

Prime Factorisation of 60,84&108 are:

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

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

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

H.C.F OF 60,84&108 IS 2^2×3=12

Therefore,12 participants can be seated in each room.

$\: No. \: of \: Rooms \: Required = \frac{total \: no. \: of \: Participants}{12}$

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

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

Hence ,the minimum number of rooms required is 21.