WordPress is number one CMS and have very useful options. You can get Home/Front Page ID by using following code
$frontpage_ID = get_option( 'page_on_front' );
Above Code will return the ID of the Home/Front page we have set for the site, or return 0 if Home/Front page hasn’t been set.
Also you can get the Blog Page ID by using following code
$blogpage_ID = get_option( 'page_for_posts' );