Apply filters on date format

As per the code reference the_time filter recieves two parameters – $get_the_time and $format. You can use the latter to determine which formatting option to use.

add_filter( 'the_time', 'changer_date_format', 10, 2 );
function changer_date_format( $ladate, $format ) {
  global $post;
  if ( 'd M' === $format ) {
    return get_post_time( get_option( 'date_format' ), false, $post, true ); 
  } else if ( 'H:i' === $format ) {
    return get_post_time( get_option( 'time_format' ), false, $post, true ); 
  } else {
    return $ladate;
  }  
}