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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 . - Mathematics

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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

Minimum number of rooms required = `"π‘‡π‘œπ‘‘π‘Žπ‘™ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘Žπ‘Ÿπ‘‘π‘–π‘π‘–π‘π‘Žπ‘›π‘‘π‘ " /"𝐻𝐢𝐹 (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.

Concept: Euclid’s Division Lemma
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