Answer
LCM = $x^{3}(2x-1)^{2}$
Work Step by Step
Step 1:
Factor each polynomial completely.
$ 4x^{3}-4x^{2}+x=x(4x^{2}+4x+1)=\qquad$
... recognize perfect square
$=\boxed{x(2x-1)^{2}}$
$2x^{3}-x^{2}=\boxed{x^{2}(2x-1)}$
$x^{3}=\boxed{x^{3}}$
Step 2:
The LCM is the product of each of these factors raised to a power equal to the greatest number of times that the factor occurs in the polynomials.
LCM = $x^{3}(2x-1)^{2}$
