Pairwise Products

Algebra Level 2

\[\large xy = 24 \quad xz = 30 \quad yz = 15\]

If \(x,y,z\) are positive, then \(x + y + z\) can be written as \(\frac{a\sqrt{b}}{c}\), where \(a,b\) and \(c\) are positive integers, with \(a\) and \(c\) are relatively prime, and \(b\) is square-free. Find \(a+b+c\).

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