What is lcm 36(x^3+x^2*y-12x*y^2),54(x^3*y+4x^2*y^2-21x*y^3) ?

The solution to lcm 36(x^3+x^2*y-12x*y^2),54(x^3*y+4x^2*y^2-21x*y^3) is 108xy(x+4y)(x+7y)(x-3y)

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lcm 36(x^3+x^2y-12xy^2),54(x^3y+4x^2y^2-21x*y^3)

lcm

36 (x^{3} + x^{2} \cdot y - 12 x \cdot y^{2}), 54 (x^{3} \cdot y + 4 x^{2} \cdot y^{2} - 21 x \cdot y^{3})

108 x y (x + 4 y) (x + 7 y) (x - 3 y)

Solution steps

Find Least Common Multiplier of

36 (x^{3} + x^{2} \cdot y - 12 x \cdot y^{2}), 54 (x^{3} \cdot y + 4 x^{2} \cdot y^{2} - 21 x \cdot y^{3})

Factor

36 (x^{3} + x^{2} \cdot y - 12 x \cdot y^{2}) : 2^{2} \cdot 3^{2} x (x + 4 y) (x - 3 y)

Factor

54 (x^{3} \cdot y + 4 x^{2} \cdot y^{2} - 21 x \cdot y^{3}) : 2 \cdot 3^{3} x (x + 7 y) (x - 3 y) y

Multiply each factor with the highest power:

2^{2} \cdot 3^{3} \cdot x \cdot (x + 4 y) \cdot (x + 7 y) \cdot (x - 3 y) \cdot y

Simplify

108 x y (x + 4 y) (x + 7 y) (x - 3 y)

x^{2} - 3 x +, 2 x^{2} - 9 x^{2}

4 a + 6 b + 5 c, - 3 a - 9 b, a + 3 b - 4 c

\frac{5}{( x - 7 )}, \frac{3}{( x - 2 )}

x^{2} - 4, x^{3} - 8, x^{2} + 2 x + 4

(13), (\frac{1 a}{3}), (36), (33 b), (48)

What is lcm 36(x^3+x^2*y-12x*y^2),54(x^3*y+4x^2*y^2-21x*y^3) ?
The solution to lcm 36(x^3+x^2*y-12x*y^2),54(x^3*y+4x^2*y^2-21x*y^3) is 108xy(x+4y)(x+7y)(x-3y)