Solve {l}{-m-n-p}{+m+2n+0-5}{-6m+0+3p+4}{5m+2n+0-8}

$$\left. \begin{array} { l } { - m - n - p } \\ { + m + 2 n + 0 - 5 } \\ { - 6 m + 0 + 3 p + 4 } \\ { 5 m + 2 n + 0 - 8 } \end{array} \right.$$

Least Common Multiple

$$\left(5-2n-m\right)\left(6m-3p-4\right)\left(5m+2n-8\right)\left(m+n+p\right)$$

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.

$$\left(5-2n-m\right)\left(6m-3p-4\right)\left(5m+2n-8\right)\left(m+n+p\right)$$

Expand the expression.

$$-30m^{4}+218m^{3}-96m^{2}n^{2}+15m^{2}p^{2}-372m^{2}-24mn^{3}+220mn^{2}+36mnp^{2}+27mnp-476mn-99mp^{2}+24mpn^{2}-252mp+160m+16n^{3}+12n^{2}p^{2}-104n^{2}-102nm^{3}+422nm^{2}-78np^{2}-21npm^{2}+16np+160n+120p^{2}-15pm^{3}+119pm^{2}+12pn^{3}-62pn^{2}+160p$$

Evaluate

$$-m-n-p,\ m+2n-5,\ 4+3p-6m,\ 5m+2n-8$$