What is lcm x^2+2x+1,3x^3+x^2+2x+5 ?

The solution to lcm x^2+2x+1,3x^3+x^2+2x+5 is (3x^3+x^2+2x+5)(x+1)^2

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lcm x^2+2x+1,3x^3+x^2+2x+5

lcm

x^{2} + 2 x + 1, 3 x^{3} + x^{2} + 2 x + 5

(3 x^{3} + x^{2} + 2 x + 5) (x + 1)^{2}

Solution steps

Find Least Common Multiplier of

x^{2} + 2 x + 1, 3 x^{3} + x^{2} + 2 x + 5

Factor

x^{2} + 2 x + 1 : (x + 1)^{2}

Multiply each factor with the highest power:

(3 x^{3} + x^{2} + 2 x + 5) \cdot (x + 1)^{2}

2 + 3, (2 x + 3)

\frac{4}{3} \cdot x^{2}, - \frac{1}{2} \cdot x, \frac{6}{5} \cdot x^{3}

3 a - 2 b + c, 5 a + 8 b - 7 c

(4 x^{4}), (3 x^{3})

\frac{x}{2}, \frac{y}{2}

What is lcm x^2+2x+1,3x^3+x^2+2x+5 ?
The solution to lcm x^2+2x+1,3x^3+x^2+2x+5 is (3x^3+x^2+2x+5)(x+1)^2