Columns("M:M").RemoveDuplicates Columns:=1, Header:=xlYes
The number of rows does not need to be pre-determined. You can apply it to the whole column.
And if you use the Macro Recorder as you record yourself using this functionality, you can get most of the code you need.
Here is a cleaned-up version that removes duplicates from column M:
Code:Columns("M:M").RemoveDuplicates Columns:=1, Header:=xlYes