Determine the index of the radical and each fraction. The index is a small superscript located in the upper left portion of the radical symbol. If no index is present, it is assumed to be 2.
Raise both fractions to an exponent equal to the respective indexes on the radical symbols. This has the effect of removing the radicals from the fraction.
Determine the greatest common factor between the denominators within the fractions. The greatest common factor is the largest multiple shared by both denominators. For example, if the denominators were 12 and 144, the greatest common factor would be 12.
Multiply the denominators of each fraction.
Divide the resulting value by the greatest common factor. The resulting value is the LCD of both fractions.