How can I display *only* the child category of a product?

I was directed to this post – which solved my problem 100%. Here is the solution I used from that post.

// get all product cats for the current post
$categories = get_the_terms( get_the_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.
          echo $category->name;
      }
    endforeach;

endif;