Foundation
Mathematics Foundation
HCF and LCM
Properties of Real Number
Rational Numbers
Question
In a seminar, the number of participants in Hindi, English and Mathematics are 60,84 and 108 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.
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Solution
The Number of room will be minimum if each room accomodates 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 = 22 × 3 × 5, 84 = 22 × 3 × 7 and 108 = 22 × 33
∴ HCF of 60,84 and 108 is 22 × 3 = 12
Therefore, in each room 12 participants can be seated.
Therefore, in each room 12 participants can be seated.