The biggest $\gcd(11n+4, 7n+2)$? I am having problems solving this problem with greatest common divisors:
What is the greatest common divisor of $11n+4$ and $7n +2$?
I tried Euclidean algorithm, and I tried to deduce the answer and I tried to incorporate 
$$\gcd(a,b)\cdot\mathrm{lcm}(a,b)=|ab|$$

\begin{align}
   (11n+4) &= 1(7n+2) + (4n+2) \\
   (7n+2)  &= 2(4n+2) + (-n-2) \\
   (4n+2)  &= -4(-n-2) - 6
\end{align}
This suggests that the biggest gcd must be a divisor of $6$.
Such a value should occur when $n=-2$.
\begin{align}
    11(-2)+4 &= -18 \\
     7(-2)+2 &= -12 \\
   \gcd(-18, -12) &= 6
\end{align}
