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xy=24xz=30yz=15\large xy = 24 \quad xz = 30 \quad yz = 15xy=24xz=30yz=15
If x,y,zx,y,zx,y,z are positive, then x+y+zx + y + zx+y+z can be written as abc\frac{a\sqrt{b}}{c}cab, where a,ba,ba,b and ccc are positive integers, with aaa and ccc are relatively prime, and bbb is square-free. Find a+b+ca+b+ca+b+c.
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