I remember searching for this T-SQL statement a few months ago, so time to put it on the blog.
select dateadd(m, datediff(m, 0, dateadd(MM, -1,getdate())), 0) as [Date of First Day of Last Month]
select dateadd(m, datediff(m, 0, dateadd(m, 1, dateadd(MM, -1,getdate()))), -1) as [Date of Last Day of Last Month]