We can use EOMONTH along with DATEADD to find out
First Day of given/current month. Below is the SQL query used for this calculation. It will be more useful whenever we supposed to calculate Effective & Expiration dates
DECLARE @GivenDate AS DATETIME = GETDATE()
SELECT DATEADD(DAY, 1, EOMONTH(@GivenDate, -1)) AS 'Current Month Start Date'
OutPut GivenDate Current Month Start Date
2015-03-20 12:39:34.277 2015-03-01