Solve {l}{27+x^3}{m^6+n^3}

$$\left. \begin{array} { l } { 27 + x ^ { 3 } } \\ { m ^ { 6 } + n ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$\left(x^{3}+27\right)\left(m^{6}+n^{3}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{3}+27=\left(x+3\right)\left(x^{2}-3x+9\right) n^{3}+m^{6}=\left(m^{2}+n\right)\left(m^{4}+n^{2}-nm^{2}\right)$$

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

$$\left(x+3\right)\left(m^{2}+n\right)\left(x^{2}-3x+9\right)\left(n^{2}+m^{4}-nm^{2}\right)$$

Expand the expression.

$$x^{3}m^{6}+n^{3}x^{3}+27m^{6}+27n^{3}$$

Evaluate

$$x^{3}+27,\ m^{6}+n^{3}$$