Question 22
Consider the sequence
$$
\begin{aligned}
x_{1} & = 19, \\
x_{2} & = 95, \\
x_{n+2} & = \operatorname{lcm}\left(x_{n+1}, x_{n}\right) + x_{n},
\end{aligned}
$$
for $n \gt 1$, where $\operatorname{lcm}(a, b)$ means the least common multiple of $a$ and $b$. Find the greatest common divisor of $x_{1995}$ and $x_{1996}$.
$$
\begin{aligned}
x_{1} & = 19, \\
x_{2} & = 95, \\
x_{n+2} & = \operatorname{lcm}\left(x_{n+1}, x_{n}\right) + x_{n},
\end{aligned}
$$
for $n \gt 1$, where $\operatorname{lcm}(a, b)$ means the least common multiple of $a$ and $b$. Find the greatest common divisor of $x_{1995}$ and $x_{1996}$.