Yes use the Sender object. Use the buttons tag to identify which button was pressed:
Set the same EventName in the designer, or initialize the buttons to the same EventName if you are creating them in code.
Sub Common_Click
Dim B As button = Sender
Select B.Tag
Case 1
'Do Something
Case 2
'Do Something Else
End Select
End Sub
Where 1 & 2 are values of the Tags