Problem:
Find the least common multiple of $\{-87,13,-48\}$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the least common multiple}: \\
 \text{lcm}(-87,13,-48) \\
\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}(-87,13,-48)=\text{lcm}(87,13,48) \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{l}
 \text{Find }\text{the }\text{prime }\text{factorization }\text{of }\text{each }\text{integer}: \\
 \text{The }\text{prime }\text{factorization }\text{of }\text{87 }\text{is}: \\
\end{array}
 \\
 87=3\times 29 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{The }\text{prime }\text{factorization }\text{of }\text{13 }\text{is}: \\
 13=13^1 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{The }\text{prime }\text{factorization }\text{of }\text{48 }\text{is}: \\
 48=2^4\times 3 \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the largest power of each prime factor} \\
 \text{The }\text{largest }\text{power }\text{of }2 \text{that }\text{appears }\text{in }\text{the }\text{prime }\text{factorizations }\text{is }2^4 \\
 \text{The }\text{largest }\text{power }\text{of }3 \text{that }\text{appears }\text{in }\text{the }\text{prime }\text{factorizations }\text{is }3^1 \\
 \text{The }\text{largest }\text{power }\text{of }\text{13 }\text{that }\text{appears }\text{in }\text{the }\text{prime }\text{factorizations }\text{is }13^1 \\
 \text{The }\text{largest }\text{power }\text{of }\text{29 }\text{that }\text{appears }\text{in }\text{the }\text{prime }\text{factorizations }\text{is }29^1 \\
 \text{Therefore }\text{lcm}(87,13,48)=\left(2^4\times 3^1\times 13^1\times 29^1=18096\right): \\
\end{array}
 \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \text{lcm}(-87,13,-48)=18096 \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/lcm_w_steps/4128.txt'}