Solve {l}{2x^{2}y^{3}+3xy^2}{3m^5n^2-6m^4n+m}

$$\left. \begin{array} { l } { 2 x ^ { 2 } y ^ { 3 } + 3 x y ^ { 2 } } \\ { 3 m ^ { 5 } n ^ { 2 } - 6 m ^ { 4 } n + m } \end{array} \right.$$

Least Common Multiple

$$mxy^{2}\left(2xy+3\right)\left(3n^{2}m^{4}-6nm^{3}+1\right)$$

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.

$$mxy^{2}\left(2xy+3\right)\left(3n^{2}m^{4}-6nm^{3}+1\right)$$

Expand the expression.

$$6n^{2}x^{2}y^{3}m^{5}-12nx^{2}y^{3}m^{4}+2mx^{2}y^{3}+9xn^{2}y^{2}m^{5}-18nxy^{2}m^{4}+3mxy^{2}$$

Evaluate

$$xy^{2}\left(2xy+3\right),\ m\left(3n^{2}m^{4}-6nm^{3}+1\right)$$