I don't know what you mean by "last month rent", but yes, between key money, deposit, real estate agent fee (1 month's rent), insurance and, if you're foreign, guarantor's fee, you typically pay something like 4~6 months' rent upfront.
Last month's rent means you've prepaid for the final month of your rental. In the US, if you're in a region where this is legal/accepted, when you give 30-day notice you don't owe any money for that final month.
You mean last two months' rent. The two you pay in advance.
I see. In Japan the rent is usually paid in advance anyway.
And still they wonder why some young people are very averse to moving out from their parents' homes (I'm not referencing hikikomoris, that's a whole another matter).