Finding $\operatorname{lcm}\big(t-1,(1-t)^2\big)$.

Question

I get $2$ answers for this question: $$(t-1)^2 \quad \textrm{and} \quad -(t-1)^2$$

Which one is correct ? Why ? Is it a must for the LCM to be positive? Im confused. Please help.

Answer 1

Adding on Maximillian Janisch's comment:

$(t-1)^2$ is correct, since by definition the LCM must be positive (Wikipedia).

Consider finding the LCM of $3$ and $5$. If we restrict the LCM to be positive, then $15$ is the smallest common multiple. However, if the LCM can be negative, $-15, -30, -45 \cdots$ can also be the LCM. The LCM for negative numbers is not well defined, so it has to be restricted to the positive numbers.