x, y, and z are positive integers such that gcd(x,y,z)=14 and lcm(x,y,z)=630. What is the smallest possible value of x+y+z?

x, y, and z are positive integers such that gcd(x,y,z)=14 and lcm(x,y,z)=630. What is the smallest possible value of x+y+z?

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