Infinite factorials

Number Theory Level 3

$\sqrt{6n \times \sqrt{1\sqrt{1\sqrt{1\ldots}}} \times \sqrt{2\sqrt{2\sqrt{2\ldots}}} \times \ldots \times \sqrt{n\sqrt{n\sqrt{n\ldots}}} }$

For a particular positive value of $n$ , the expression with infinitely nested radicals above can be simplified to $12n$ . What is the value of $n$ ?

24 4 12 6 15 16 3 5