# How do you find the LCM for y^3-y^2, y^4-y^2?

Oct 29, 2016

The LCM = ${y}^{4} - {y}^{2} = {y}^{2} \left(y + 1\right) \left(y - 1\right)$

#### Explanation:

The first step is to factor each expression.

${y}^{3} - {y}^{2} = \textcolor{w h i t e}{\times \times \times \times x} {y}^{2} \left(y - 1\right)$

${y}^{4} - {y}^{2} = {y}^{2} \left({y}^{2} - 1\right) = {y}^{2} \left(y + 1\right) \left(y - 1\right)$

The LCM is the product of the prime factors without any duplicates:

${y}^{3} - {y}^{2}$ is a factor of ${y}^{4} - {y}^{2}$

The LCM = ${y}^{4} - {y}^{2} = {y}^{2} \left(y + 1\right) \left(y - 1\right)$