LCM of 7x-6xy and 5xy^3-3x^2
You asked:
Find the polynomial least common multiple of the following expressions: \(- 6 x y + 7 x\), \(- 3 x^{2} + 5 y^{3} x\)
MathBot Answer:
The least common multiple is \(18 x^{2} y - 21 x^{2} - 30 y^{4} x + 35 y^{3} x\).
Begin by factoring all expressions completely. $$\begin{aligned}- 6 x y + 7 x &= - x \left(6 y - 7\right)\\- 3 x^{2} + 5 y^{3} x &= - x \left(3 x - 5 y^{3}\right)\\\end{aligned}$$
Find the least common multiple by multiplying the factors together, including only the greatest power of each common factor. \[\operatorname{lcm}(- 6 x y + 7 x, - 3 x^{2} + 5 y^{3} x) = (x)^{1}\cdot (6 y - 7)^{1}\cdot (3 x - 5 y^{3})^{1} = 18 x^{2} y - 21 x^{2} - 30 y^{4} x + 35 y^{3} x\]