Lowest common denominator of denominators (3x^4)-27x^2 and (x^3)-3x^2
First, fully factor both.
(3x^4)-27x^2 = 3x^2(x^2 - 9)
= 3x^2*(x+3)(x-3)
(x^3)-3x^2 = x^2(x-3)
The LCD is 3x^2*(x-3)(x+3).
It is the product of all factors appearing in both expressions. Factors that appear in both only appear once in the LCD.