Do you have a written agreement with the landlord? If yes, you should look in that document to see when notice must be given and when you may move out.
If you have no written agreement and assuming that this is a residential rental, WA Residential landlord-tenant act (Chapter 59.18 RCW) likely governs your rental. RCW 59.18.200 provides: "(1)(a) When premises are rented for an indefinite time, with monthly or other periodic rent reserved, such tenancy shall be construed to be a tenancy from month to month, or from period to period on which rent is payable, and shall be terminated by written notice of twenty days or more, preceding the end of any of the months or periods of tenancy, given by either party to the other." The statutes can be accessed here: http://apps.leg.wa.gov/RCW/default.aspx?cite=59.18 .
Unless you both agree to a mid-month moveout, the end of your rental likely is the "end of any of the months".
You should review your facts and options with an attorney as the specific facts of your case likely determine how your case will come out.