In a sports meet, the number of players in Football . . .

Question : In a sports meet, the number of players in Football, Hockey and Athletics are 48, 60 and 132 respectively. Find the minimum number of rooms required, if in each room the same numbers of players are to be seated and all of them being in the same sport. 

Doubt by Sachin

Solution : 

Number of players in Football = 48

Number of players in Hockey = 60

Number of players in Athletics = 132

Number of players in each room 

= HCF (48,60,132)

48 = 2⁴×3

60 = 2²×3×5

132 = 2²×3×11

HCF = 2²×3 = 12

No. of rooms required
= Total No. of Players/No. of players in each room
= (48+60+132)/12
= 240/12
= 20

Hence, the minimum number of rooms required are 12.