# Case based:1

### **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.**

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

**(a) 14 (b) 12**

**(c) 16 (d) 18**

**(B) What is the minimum number of rooms required during the event ?**

**(C) The LCM of 60, 84 and 108 is :**

**(a) 3780 (b) 3680**

**(c) 4780 (d) 4680**

**(D) The product of HCF and LCM of 60, 84 and 108 is :**

**(a) 55360 (c) 35360**

**(c) 45500 (d) 45360**

**(E) Express 108 as a product of its primes:**

**Solution:**

**(A) Answer is (b) 12**

**Explanation:-**

60 = 2 × 2 × 3 × 5

84 = 2 × 2×3 × 7

108 = 2 × 2 × 3 × 3

HCF(60, 84, 108) = 2 × 2 × 3 = 12

Hence the maximum number of participants that can be accommodated in a room is 12.

**(B) Number of rooms required by participants of subject hindi**

Similarly

Number of rooms required by participants of english

Number of rooms required by participants of Mathematics

Minimum number of rooms required

**(C) Answer is (a) 3780**

Explanation:-

60 = 2 × 2 × 3 × 5

84 = 2 × 2×3 × 7

108 = 2 × 2 × 3 × 3

LCM(60, 84, 108) = 2 × 2× 3 × 3 × 3 × 5 × 7

= 3780

**(D) Answer is (b) 45360**

Explanation :-

From parts (A) and (C)

HCF(60, 84, 108) = 12

LCM(60, 84, 108) = 3780

∴ HCF × LCM = 12 × 3780

= 45360

**(E) 108 = 2 × 2 × 3 × 3 × 3**

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