2021 Fall AMC 10B Problem 6

The least positive integer with exactly 2021 distinct positive divisors can be written in the form m \cdot 6^k, where m and k are integers and 6 is not a divisor of m. What is m+k?

(\textbf{A})\: 47\qquad(\textbf{B}) \: 58\qquad(\textbf{C}) \: 59\qquad(\textbf{D}) \: 88\qquad(\textbf{E}) \: 90

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.