Find the LCM of $2 x + 6, x^{2} + 3 x$

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Solution

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

Factorise $2 x + 6$ as follows:

$2 x + 6 = 2 (x + 3)$

Now, factorise $x^{2} + 3 x$ as follows:

$x^{2} + 3 x = x (x + 3)$

Since the least common multiple between the polynomials $2 x + 6$ and $x^{2} + 3 x$ is $2 x (x + 3)$ .

Hence, the $L C M$ is $2 x (x + 3)$ .

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