A Seminar

Number Theory Level 2

In a seminar, the number of participants in Science, English and Mathematics are 144, 180 and 192 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.

43 38 45 40

Ojasee Duble by Ojasee Duble , 19, India

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1 solution

Marco Brezzi
Aug 13, 2017

Firstly we have to find gcd ⁡ ( 192 , 144 , 180 ) \gcd(192,144,180)

gcd ⁡ ( 192 , 144 , 180 ) = gcd ⁡ ( 2 6 ⋅ 3 , 2 4 ⋅ 3 2 , 2 2 ⋅ 3 2 ⋅ 5 ) = 2 2 ⋅ 3 = 12 \gcd(192,144,180)=\gcd(2^6\cdot 3,2^4\cdot 3^2,2^2\cdot 3^2\cdot 5)=2^2\cdot 3=12

So there are 12 12 people in every room. To calculate the number of rooms

R = ( 192 + 144 + 180 ) 12 = 43 R=\dfrac{(192+144+180)}{12}=\boxed{43}

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