Get Deepest category id of a product (WooCommerce)

Get Deepest category id of a product (WooCommerce).php

<?php
/**
*
* Get deepest product category woocommerce
* @param $product_id is the id of a product
* 
*/
function prefix_get_deepest_product_category($product_id = ''){
    // get all product cats for the current post
    $categories = get_the_terms( $product_id, 'product_cat' ); 

    // wrapper to hide any errors from top level categories or products without category
    if ( $categories && ! is_wp_error( $category ) ) : 

        // loop through each cat
        foreach($categories as $category) :
          // get the children (if any) of the current cat
          $children = get_categories( array ('taxonomy' => 'product_cat', 'parent' => $category->term_id ));

          if ( count($children) == 0 ) {
              // if no children, then echo the category name.
              return $category->term_id;
          }
        endforeach;

    endif;
}