If I have a month-to month lease and was told by my landlord that even though I'm moving out this month I still need to pay for the following month is that true?

Question Details:

I have to give 30 days notice in writing that I'm moving. I was told I couldn't do it in the middle of the month, that I had to do it on the first. I'm moving out on the 20th, so I won't be living there anymore, am I legally obligated to pay for the full month next month even though the apartment will be vacant? I also never received a copy of my lease and I've been living there for almost 2 years.

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