Question

find the least common multiple of x^3-x^2+x-1and x^2-1

Answer 1

@A1B2C3_
Example:
Least common multiple (LCM) works as follows, using numbers as example:
LCM of
\(12=\color{red}{2*2}*\color{green}{3}\)
\(18= \color{green}{2}*\color{red}{3*3}\)
Least common multiple is the smallest number that contains the factors of each number,
namely \(\color{red}{2*2*3*3}\). The green factors have been absorbed in the red factors, and need not be repeated.

If you can factor the two expressions, you can work out the LCM in a similar way.

Answer 2

soo it would be(x+1)(x-1)(x^2+1)

Answer 3

Hint to factor the cubic:
x^3-x^2+x-1 = x^2(x-1) + (x-1)
Hint to factor the quadratic:
difference of two squares.