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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 .
Solution
Minimum number of rooms required = `"๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐ก๐๐๐๐๐๐๐ก๐ " /"๐ป๐ถ๐น (60,84,108)"`
Prime factorization of 60, 84 and 108 is:
60 = 22 × 3 × 5
84 = 22 × 3 × 7
108 = 22 × 33
HCF = product of smallest power of each common prime factor in the numbers = 22 × 3 = 12
Total number of participants = 60 + 84 + 108 = 252
Therefore, minimum number of rooms required = `252/12 `= 21
Thus, minimum number of rooms required is 21.
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