What kind of “hashmo’as kol” is there with a washing machine? They’re not that loud! Hashmo’as kol is about a mill or something equally noisy, where any passerby in the street can hear it going, and will think that you’re doing melocho on Shabbos. (And even that is allowed if there are no Jews within a techum shabbos, who might walk by.)
But it should be emphasized that you cannot remove the laundry from the washing machine on Shabbos, to dry it. Once the machine turns itself off you have to leave the clothes there a whole shabbos, and I don’t think that’s such a great idea for the clothes. Hanging the clothes to dry is ossur mishum mar’is ho’ayin (this is the classic case of “afilu bechadrei chadorim ossur”).