fill a range with formula, hundreds of rows down

Hi. I'd like to apply the =LOWER() function to a range of values in order to convert them from mixed case to all lower case. The values exist in column A. My thinking is to create empty column B, and apply the =LOWER(A) in column B. This works easily in cell B1 but I'd like to avoid manually 'dragging' the formula downward to bottom of the range of source data in column A. Is there any way to automate applying the formula in column B instead of dragging the formula in column B downward all the way to the bottom? (maybe based on the existence of values in in Column A?) Thank you in advance.

Thank you for your advice. This worked great!