Solve {l}{216b^{3}-343}{x^3-1000}{8+27m^3}{512b^3-9y^3}

$$\left. \begin{array} { l } { 216 b ^ { 3 } - 343 } \\ { x ^ { 3 } - 1000 } \\ { 8 + 27 m ^ { 3 } } \\ { 512 b ^ { 3 } - 9 y ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$-884736x^{3}b^{6}[phone]y^{3}-2985984b^{6}\left(mx\right)^{3}+52488\left(bmxy\right)^{3}+15552\left(bxy\right)^{3}+4741632\left(bmx\right)^{3}-83349\left(mxy\right)^{3}-52488000\left(bmy\right)^{3}[phone]m^{3}b^{6}+1404928\left(bx\right)^{3}[phone]\left(my\right)^{3}-24696\left(xy\right)^{3}-15552000\left(by\right)^{3}-4741632000\left(bm\right)^{3}[phone]b^{6}-1404928000b^{3}$$

Solution Steps

Factor the expressions that are not already factored.

$$216b^{3}-343=\left(6b-7\right)\left(36b^{2}+42b+49\right) x^{3}-1000=\left(x-10\right)\left(x^{2}+10x+100\right) 27m^{3}+8=\left(3m+2\right)\left(9m^{2}-6m+4\right)$$

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

$$52488b^{3}m^{3}x^{3}y^{3}+15552b^{3}x^{3}y^{3}+4741632b^{3}m^{3}x^{3}-83349m^{3}x^{3}y^{3}+1404928b^{3}x^{3}-24696x^{3}y^{3}-2985984m^{3}x^{3}b^{6}-884736x^{3}b^{6}-52488000b^{3}m^{3}y^{3}[phone]m^{3}y^{3}-15552000b^{3}y^{3}[phone]y^{3}[phone]m^{3}b^{6}-4741632000b^{3}m^{3}[phone]b^{6}-1404928000b^{3}$$

Evaluate

$$216b^{3}-343,\ x^{3}-1000,\ 27m^{3}+8,\ 512b^{3}-9y^{3}$$