Find the LCM of $x^{2} y + x y^{2}, x^{2} + x y$

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Solution

We know that $L C M$ is the least common multiple.

Factorise $x^{2} y + x y^{2}$ as follows:

$x^{2} y + x y^{2} = x y (x + y)$

Now, factorise $x^{2} + x y$ as follows:

$x^{2} + x y = x (x + y)$

Since the least common multiple between the polynomials $x^{2} y + x y^{2}$ and $x^{2} + x y$ is $x y (x + y)$ .

Hence, the $L C M$ is $x y (x + y)$ .

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