Question

Case Study:
A 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.

(i) What is the minimum number of rooms required during

the event?

(ii) 108 can be expressed as a product of its primes as

(iii) The product of HCF and LCM of 60, 84, and 108 is

Answer 1

(i) The Number of rooms will be minimum if each room accommodates maximum number of participants. Since in each room the same number of participants are to be seated and all of them must be of the same subject.

Therefore, the number of participants in each room must be the HCF of 60,84 and 108. The prime factorisations of 60,84 and 108 are as under.

60 = $2^2$×3×5,

84 = $2^2$×3×7,

108 = $2^2$×(3^3),

HCF of 60,84 and 108 is $2^2$×3 = 12 >

Therefore, in each room 12 participants can be seated.

Number of rooms required = (Total number of participants )/12,

Number of rooms required = (60 + 84 + 108)/12,

Number of rooms required = 252/12 = 21

(ii)

We are asked to expressed 108 as its product of primes,

108 = 2×2×3×3×3 =$2^2$× $3^3$

(iii) We already have HCF value of given number,

HCF of 60,84 and 108 is $2^2$×3 = 12 >

We need to calculate the LCM value of said numbers so that we could get the required answer,

60 = $2^2$×3×5,

84 = $2^2$×3×7,

108 = $2^2$×$3^3$,

LCM = (2^2)×(3^3)×5×7

LCM = 3780,

HCF×LCM = 12×3780,

HCF×LCM = 45360