Wordpress - Get the ID of the latest post

$latest_cpt = get_posts("post_type=yourcpt&numberposts=1");
echo $latest_cpt[0]->ID

The only cheaper way than above, I can think of, would be to write your own SQL query to just return the one post and only the column ID.

A more pure SQL way:

function GetLastPostId()
{
    global $wpdb;

    $query = "SELECT ID FROM $wpdb->posts ORDER BY ID DESC LIMIT 0,1";

    $result = $wpdb->get_results($query);
    $row = $result[0];
    $id = $row->ID;

    return $id;
}