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+1 vote
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in Number System by (29.8k points)
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A seminar is being conducted by an Educational Organization, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.

1. In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are 

a) 14

b) 12

c) 16

d) 18

2. What is the minimum number of rooms required during the event?

a) 11

b) 31

c) 41

d) 21

3. The LCM of 60, 84 and 108 is

a) 3780

b) 3680

c) 4780

d) 4680

4. The product of HCF and LCM of 60,84 and 108 is

a) 55360

b) 35360

c) 45500

d) 45360

5. 108 can be expressed as a product of its primes as

a) 23 x 32

b) 23 x 33

c) 22 x 32

d) 22 x 33

2 Answers

+1 vote
by (46.5k points)
selected by
 
Best answer

1. b) 12

Maximum number of participants in each room will be the

HCF of 60, 84, 108

So,

Thus, HCF = 2 x 2 x 3

= 12

2. d) 21

Given that

Number of participants in Hindi, English and Mathematics are 60, 84
and 108 respectively.

And, in each room, maximum 12 participants can be accommodated

Thus,

Minimum Number of rooms = Total Participants / Max Participants in one room

= 252/12

= 21 rooms

3. a) 3780

LCM of 60, 84 and 108

LCM = 2 x 2 x 3 x 3 x 3 x 5 x 7

= 3780

4. d) 45360

Product of LCM and HCF of 60, 84 and 108

HCF x LCM = 12 x 3780

= 45360

5. d) 22 x 33

Doing Prime Factorisation of 108

36 = 2 x 2 x 3 x 3 x 3

= 22 x 33

+2 votes
by (28.9k points)

1. b) 12

2. d) 21

3. a) 3780

4. d)45360

5. d) 22 x 33

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