HELP with CTE or a Cursor to update multiple rows in 1 table ..selecting from Multiple databases

olafhelper : thank you for looking ..please see below..

SQL Server Instance=A
Dbname=ABC
SELECT * from Table1
Dbname productid
ABC 123

SQL Server Instance=A
Dbname=XYZ
SELECT * from Table2
Dbname productid
XYZ 987



SQL Server Instance=A
Dbname=AQW
SELECT * from Table3
Dbname productid
AQW 123456


Like we have 1000 DB's in Server A and each db has a table which hold productid's

1 Main LOGIN info table in Server A
Dabatase DB1
SELECT * from DB1. DBO.LOGIN table
DBName product ID
ABC NULL
XYZ A9065
AQW 33c@1442

these rows in 1 main Login table are not matching the tables( Table1, table2, tale3) rows of each individual Databases

Now I want to update 1 Main LOGIN info table in Server A Dabatase DB1, so that I get results matching each login table of all db's
SELECT * from DB1. DBO.LOGIN table
DBName product ID
ABC 123
XYZ 987
AQW 123456