2016 AMC 12B Problem 24

There are exactly 77,000 ordered quadruples $(a,b,c,d)$ such that $\gcd(a,b,c,d) = 77$ and $\text{lcm}(a,b,c,d)=n$ . What is the smallest possible value of $n$ ?

Check out the whole set: 2016 AMC 12B Problems .