Wordpress; updated SQL query code for a very small function

I need a custom Wordpress function that will return an array of oldest values from the database. For this example; I have created a bunch of custom posts ('machine') in Wordpress. Each custom post has been assigned two custom metadata keys; 'last_updated_timestamp' and 'serial_number'. Timestamps are in epoch format (i.e. '1557240847'). This is the code that I have so far, and it returns an array of serial numbers as expected. Although, I need the SQL query updated, as to instead return the OLDEST serial numbers found in the database, based on their metadata keys 'last_updated_timestamp'. function get_oldest_serial_numbers($limit = 10) { global $wpdb; $result = $wpdb->get_col( $wpdb->prepare(" SELECT pm.meta_value FROM {$wpdb->postmeta} pm LEFT JOIN {$wpdb->posts} p ON [login to view URL] = pm.post_id WHERE pm.meta_key = 'serial_number' AND p.post_status = 'publish' AND p.post_type = 'machine' LIMIT %d ",$limit)); return $result; }