Minimum and Maximum Values Using Lagrange Multipliers

Example question on using Lagrange Multipliers to find the min/max or optimize a multivariable calculus question. Find a,b,c so that the volume (4/3)pi(abc) of the ellipsoid (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) = 1 passing through the point (1,2,1) is as small as possible.