Solve {l}{m^2(kt^2)^2-3m(k^2t)}{(2m-k)(3k-2m)}

$$\left. \begin{array} { l } { m ^ { 2 } ( k t ^ { 2 } ) ^ { 2 } - 3 m ( k ^ { 2 } t ) } \\ { ( 2 m - k ) ( 3 k - 2 m ) } \end{array} \right.$$

Least Common Multiple

$$mt\left(2m-k\right)\left(2m-3k\right)k^{2}\left(mt^{3}-3\right)$$

Solution Steps

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$mt\left(2m-k\right)\left(2m-3k\right)k^{2}\left(mt^{3}-3\right)$$

Expand the expression.

$$4k^{2}m^{4}t^{4}-8k^{3}m^{3}t^{4}+3m^{2}k^{4}t^{4}-9mtk^{4}-12tk^{2}m^{3}+24tm^{2}k^{3}$$

Evaluate

$$mtk^{2}\left(mt^{3}-3\right),\ \left(2m-k\right)\left(3k-2m\right)$$