It's obvious that all terms are divisible by 19.
I now use induction to show that the gcd of any two consecutive terms must be 19.
(x1,x2)=19
Assume for n<=k, (x_(n-1),xn)=19
Since (x_(n-1),xn)=19,
write x_(n-1)=19a, x_n=19b, where (a,b)=1, then
x_(n+1)=lcm(19a,19b)+19a=19ab+19a=19a(1+b)
since (a,b)=1, (b,b+1)=1
gcd (xn,x_(n+1))=1
which finishes the induction.
So (x1995,x1996)=19

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