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The greatest common divisor of two integers is \((x+2)\)  and their least common multiple is , where \(x(x+2)\)  is a positive integer. If one of the integers is 24, what is the smallest possible value of the other one?

 Oct 31, 2018
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solve gcd(24, n) = x + 2 lcm(24, n) = x (x + 2) for n

 

n = 6  and x =4, so that:

GCD(24, 6) =4+2 =6

LCM(24,6) =4(4+2) =24

 Oct 31, 2018

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