Very odd reciprocals

The smallest possible positive value of 1(1w+1x+1y+1z)1-\left( \frac{1}{w} + \frac{1}{x} +\frac{1}{y} +\frac{1}{z} \right) where w, x, y, zw,\ x,\ y,\ z are odd positive integers, has the form ab\frac {a}{b}, where a,ba, b are coprime positive integers. Find a+ba+b.

Note: The problem does not state that w,x,y,zw, x, y, z must be distinct.

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