Just a continuation from mozboz’ answer. For those curious as I was, you could use the date() or date_i18n() functions to format the date properly in the following snippet.
function get_latest_update_date() {
global $wpdb;
$thelatest = $wpdb->get_var("SELECT max(post_modified) FROM wp_posts WHERE post_type IN ('post', 'page');");
//returns formatted date like 13.08.2001
return date_i18n('j.m.Y', strtotime($thelatest));
}
add_shortcode('latestupdatedate', 'get_latest_update_date');