UPDATE `prices` AS `prc`
JOIN (
SELECT `prd`.`parent_id` AS `product_id`, MIN(`prc`.`price`) AS `price`
FROM `products` AS `prd`
JOIN `prices` AS `prc` ON `prc`.`product_id` = `prd`.`product_id`
GROUP BY `prd`.`parent_id`
) AS `min` ON `min`.`product_id` = `prc`.`product_id`
SET `prc`.`price` = `min`.`price`