I don't think I've ever had to pay first and last month's rent plus a security deposit.
I've paid first month's rent and a security deposit which was equal to one month's rent, but nothing that was ever specified as "last month's rent". Rent on my apartment has gone up $155 per month since I moved in (which isn't even close to the increases some people have seen), so it wouldn't make sense for a landlord to say "pay me for the last month right now", because they'd be losing money for the month after you give your notice.
In Alberta, the maximum amount of a security deposit is one month's rent, and it is fully refundable (with interest) when the tenant moves out (assuming the landlord doesn't have to use part of it to repair any damage the tenant may have caused over and above normal wear and tear).
This site seems to have some good information (in plain English) about the Alberta Landlord Tenant Act:
http://tenant.landlordandtenant.org/home/default.aspx