Question 24There 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?$$13{,}860$$20{,}790$$21{,}560$$27{,}720$$41{,}580$