You can retrieve the parent Category id of a post by using the following function.

function get_posts_parent_category_id(){
$category = get_the_category();
$cat = get_category($category[0]->term_id);
return $parent_catid = $cat->category_parent;

Place the above code in function.php in your theme folder or place it in the function.php in the wp-include folder (to use the function in any theme).

From any page, simply call the function and get the parent category id in a variable like this.

$parent_catid = get_posts_parent_category_id();

Now you have the parent category id in $parent_catid variable

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