Question

# Find the least common multiple of x^{3}-x^{2}+x-1 and x^{2}-1. Write the answer in factored form.

Factors and multiples
Find the least common multiple of $$x^{3}-x^{2}+x-1\ and\ x^{2}-1$$. Write the answer in factored form.

$$x^{3}-x^{2}+x-1=x^{2}(x-1)+(x-1)$$
$$=x(-1)(x^{2}+1)$$
$$x^{2}-1=(x(-1)(x+1)$$
The lowest common multiple is the product of all the factors of each polynomial to the highest degree. Each of the factors $$x-1$$, and $$x^{2}+1$$ all have a degree of 1 so the lowest common multiple is $$(x-1)(x+1)(x^2+1)$$.