I lives in my apartment more than 1 year. My landlord gives me 60 days noticed to move out, so they can reconstructions a whole units. My landlord also wants to collect the rent up to the last day I leave. Do I have to pay my rents for the next 60 days?

Thanks,

If you are living there for 60 days, then yes you have to pay rent for 60 days. UNLESS your deposit (when you moved in) included the last month of rent.

I agree. You cannot apply the deposit to the last month's rent without agreement of the landlord.