Solve {l}{x^{2}b+ab^2+ab}{12ab+16ab^2+20a^2b^2}

$$\left. \begin{array} { l } { x ^ { 2 } b + a b ^ { 2 } + a b } \\ { 12 a b + 16 a b ^ { 2 } + 20 a ^ { 2 } b ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$4ab\left(5ab+4b+3\right)\left(x^{2}+ab+a\right)$$

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.

$$4ab\left(5ab+4b+3\right)\left(x^{2}+ab+a\right)$$

Expand the expression.

$$20a^{2}b^{2}x^{2}+16ab^{2}x^{2}+12abx^{2}+20a^{3}b^{3}+16a^{2}b^{3}+20b^{2}a^{3}+28a^{2}b^{2}+12ba^{2}$$

Evaluate

$$b\left(x^{2}+ab+a\right),\ 4ab\left(5ab+4b+3\right)$$