Find the LCM of $m^{2} - n^{2}, 3 m^{2} - 3 m n$

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Solution

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

Factorise $m^{2} - n^{2}$ as follows:

$m^{2} - n^{2} = (m + n) (m - n)$ (using identity $a^{2} - b^{2} = (a + b) (a - b)$ )

Now, factorise $3 m^{2} - 3 m n$ as follows:

$3 m^{2} - 3 m n = 3 m (m - n)$

Since the least common multiple between the polynomials $m^{2} - n^{2}$ and $3 m^{2} - 3 m n$ is $3 m (m + n) (m - n)$ .

Hence, the $L C M$ is $3 m (m + n) (m - n)$ .

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