Use SQLCMD for this....

In MS Management Stusio(SSMS), you will find SQLCMD Mode under the Query menu....

Use the following script -

:setvar defaultserver

:connect $(defaultserver)

USE [master]

GO

select serverproperty('productversion'),

serverproperty('productlevel'),

serverproperty('edition')

Just change the server name and execute.....hope this helps!

Note: The windows login needs to have administrative privileges on all the servers......also if you have multiple instances use ....for example SON1843\sql