VBA - Auto Fill always to Last Row

Bit of a VBA Novice.

I am trying to autofill a cell always to the last row available.

Here is what I have - but is not going all the way to end.

LastRow = Range("E" & Rows.Count).End(xlUp).Row
ActiveCell.FormulaR1C1 = "'001"
Range("E2").Select
Selection.AutoFill Destination:=Range("E2:E" & LastRow), Type:=xlFillCopy