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Can I give her 30 days notice and then change the locks?
Yes and no. If you took over the tenancy from the original tenant then you are a subtenant and anyone you rented to is a sub subtenant with you being their landlord. So if there are no written leases, your tenants are month to month under an oral tenancy agreement.
So you can give them a written 30 day notice to vacate but then would have to pursue a formal legal eviction through the courts if they don't vacate within that 30 days. You can't lock them out without a written lease that has that as a specific "lock out clause" or you would be guilty of an illegal eviction and they could end up suing you for breach.
As an aside, in addition to being an attorney, I have also been a landlord for over 26 years...