How does a block of cells in a column have the same value based on a drop down selection

Hello,

I'd like to know how I can have a selected block of cells in a column containing a drop down box have a value based on what's selected in the drop down box.

For instance I have a drop down box with options 1, 2, and 3 for cells A1:A20 and if I select cells A1:A5 only and select 3 in the top-most (if I had selected the cells from top to bottom) or bottom-most cell (selecting from bottom to top), that single cell changes to 3 and not rest of the selected cells. The only way I can get this to work is if I select the block of cells in the column from top to bottom so that the drop down box arrow is at the top and press ctrl+d after making the selection, but is there an automated or more simpler method that a ctrl+d isn't necessary?

Thanks