In a seminar, the number of participants in Mathematics, Physics and Chemistry are 60, 96 and 144 respectively. Find the number of rooms required if in each room, the same number of ‘ participants are to be seated and all of them are to be in the same subject.
The number of participants in each room must be the HCF of 60, 96 and 144.
∴ 60 = 2 × 2 × 3 × 5
96 = 2 × 2 × 2 × 2 × 2 × 3
144 = 2 × 2 × 2 × 2 × 3 × 3
HCF = 2 × 2 × 3 = 12
Number of rooms required
= 6012 + 9612 + 14412
= 5 + 8 + 12 = 25
Hence, number of participants = 12
in each room and number of rooms required = 25.