Find the smallest volume bounded by the coordinate planes and by a tangent plane to the ellipsoid $$ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=1. $$ The original answer is in the format $\frac{1}{2} \sqrt{3} abc$, Let abc=2 \ sqrt {3}, find the value of V.

Let's think step by step and output the final answer within \boxed{}.
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