Solve {l}{x^{3}+x^4}{3x^2+4x^3}{6x+12x^2}{6+24x}{24}

$$\left. \begin{array} { l } { x ^ { 3 } + x ^ { 4 } } \\ { 3 x ^ { 2 } + 4 x ^ { 3 } } \\ { 6 x + 12 x ^ { 2 } } \\ { 6 + 24 x } \\ { 24 } \end{array} \right.$$

Least Common Multiple

$$24\left(x+1\right)\left(2x+1\right)\left(4x+1\right)\left(4x+3\right)x^{3}$$

Solution Steps

Factor the expressions that are not already factored.

$$6+24x=6\left(4x+1\right) 24=2^{3}\times 3$$

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

$$24\left(x+1\right)\left(2x+1\right)\left(4x+1\right)\left(4x+3\right)x^{3}$$

Expand the expression.

$$768x^{7}+1920x^{6}+1680x^{5}+600x^{4}+72x^{3}$$

Evaluate

$$\left(x+1\right)x^{3},\ \left(4x+3\right)x^{2},\ 6x\left(2x+1\right),\ 6\left(4x+1\right),\ 24$$