Find the L.C.M. of $m^{4} + 3 m^{3} - m - 3$ and $m^{3} + m^{2} - 5 m + 3$ .

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Solution

$∴ H C F = H = m^{2} + 2 m - 3$
$∴ L = \frac{A \times B}{H} = A \times \frac{B}{H}$
Now $L = (m^{3} + m^{2} - 5 m + 3) \times \frac{(m^{4} + 3 m^{3} + 0 m^{2} - m - 3)}{(m^{2} + 2 m - 3)}$
$∴ L = A \times \frac{B}{H}$
$L = (m^{3} + m^{2} - 5 m + 3) (m^{2} + 2 m - 3)$

OR
$L = \frac{A}{H} \times B = \frac{(m^{3} + m^{2} - 5 m + 3)}{(m^{2} + 2 m - 3)} \times (m^{4} + 3 m^{3} + 0 m^{2} - m - 3)$
$∴ L = (m - 1) (m^{4} + 3 m^{3} - m - 3)$

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