Solve {l}{x^2-7x-30}{x^2-18x-40}{x^2+5x-24}{x^2-19x+60}

$$\left. \begin{array} { l } { x ^ { 2 } - 7 x - 30 } \\ { x ^ { 2 } - 18 x - 40 } \\ { x ^ { 2 } + 5 x - 24 } \\ { x ^ { 2 } - 19 x + 60 } \end{array} \right.$$

Least Common Multiple

$$\left(x-20\right)\left(x-15\right)\left(x-10\right)\left(x-4\right)\left(x+2\right)\left(x+8\right)\left(x^{2}-9\right)$$

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.

$$\left(x-20\right)\left(x-15\right)\left(x-10\right)\left(x-4\right)\left(x-3\right)\left(x+2\right)\left(x+3\right)\left(x+8\right)$$

Expand the expression.

$$x^{8}-39x^{7}+347x^{6}+2267x^{5}-33924x^{4}+13156x^{3}+468480x^{2}-273600x-1728000$$

Evaluate

$$\left(x-10\right)\left(x+3\right),\ \left(x-20\right)\left(x+2\right),\ \left(x-3\right)\left(x+8\right),\ \left(x-15\right)\left(x-4\right)$$