\[ \large \int_0^1 \int_0^2 \int_0^3 \left( x \ \ln(xyz) \right) \, dx \, dy \, dz \]

If the expression above equals to \(a \ln(b) - c\) for integers \(a,b,c\) with \(b\) square free, find the value of \(abc\).

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