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Let $x$ and $y$ be positive integer such that $2(x+y)=gcd(x,y)+lcm(x,y)$. Find the value of $\frac{lcm(x,y)}{gcd(x,y)}$.
Number Theory
GCD
BdMO
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Let $x$ and $y$ be positive integer such that $2(x+y)=gcd(x,y)+lcm(x,y)$. Find the value of $\frac{lcm(x,y)}{gcd(x,y)}$.