Problem:
Find the least common multiple of $\{-1,1,-2\}$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the least common multiple}: \\
 \text{lcm}(-1,1,-2) \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{Any }\text{multiple }\text{of }\text{a }\text{negative }\text{number }\text{is }\text{also }\text{a }\text{multiple }\text{of }\text{its }\text{absolute }\text{value}: \\
 \text{lcm}(-1,1,-2)=\text{lcm}(1,1,2) \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Ignore }\text{duplicate }\text{arguments }\text{in }\text{the }\text{lcm}: \\
 \text{lcm}(1,1,2)=\text{lcm}(1,2) \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Any }\text{multiple }\text{of }\text{a }\text{non-zero }\text{number }\text{is }\text{also }\text{a }\text{multiple }\text{of }1. \text{For }\text{this }\text{reason }\text{we }\text{can }\text{ignore }1 \text{when }\text{finding }\text{the }\text{lcm}: \\
 \text{lcm}(1,2)=\text{lcm}(2) \\
\end{array}
 \\
 
\begin{array}{l}
 \text{The }\text{smallest }\text{multiple }\text{of }\text{a }\text{number }\text{is }\text{itself}: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \text{lcm}(2)=2 \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/lcm_w_steps/1085.txt'}