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Either of the two samples below will work:

SELECT  MAX(date_columns) AS max_date
FROM    ( (SELECT   date1 AS date_columns
           FROM     data_table         )
          UNION
          ( SELECT  date2 AS date_columns
            FROM    data_table
          )
          UNION
          ( SELECT  date3 AS date_columns
            FROM    data_table
          )
        ) AS date_query

The second is an add-on to lassevk'slassevk's answer.

SELECT  MAX(MostRecentDate)
FROM    ( SELECT    CASE WHEN date1 >= date2
                              AND date1 >= date3 THEN date1
                         WHEN date2 >= date1
                              AND date2 >= date3 THEN date2
                         WHEN date3 >= date1
                              AND date3 >= date2 THEN date3
                         ELSE date1
                    END AS MostRecentDate
          FROM      data_table
        ) AS date_query 

Either of the two samples below will work:

SELECT  MAX(date_columns) AS max_date
FROM    ( (SELECT   date1 AS date_columns
           FROM     data_table         )
          UNION
          ( SELECT  date2 AS date_columns
            FROM    data_table
          )
          UNION
          ( SELECT  date3 AS date_columns
            FROM    data_table
          )
        ) AS date_query

The second is an add-on to lassevk's answer.

SELECT  MAX(MostRecentDate)
FROM    ( SELECT    CASE WHEN date1 >= date2
                              AND date1 >= date3 THEN date1
                         WHEN date2 >= date1
                              AND date2 >= date3 THEN date2
                         WHEN date3 >= date1
                              AND date3 >= date2 THEN date3
                         ELSE date1
                    END AS MostRecentDate
          FROM      data_table
        ) AS date_query 

Either of the two samples below will work:

SELECT  MAX(date_columns) AS max_date
FROM    ( (SELECT   date1 AS date_columns
           FROM     data_table         )
          UNION
          ( SELECT  date2 AS date_columns
            FROM    data_table
          )
          UNION
          ( SELECT  date3 AS date_columns
            FROM    data_table
          )
        ) AS date_query

The second is an add-on to lassevk's answer.

SELECT  MAX(MostRecentDate)
FROM    ( SELECT    CASE WHEN date1 >= date2
                              AND date1 >= date3 THEN date1
                         WHEN date2 >= date1
                              AND date2 >= date3 THEN date2
                         WHEN date3 >= date1
                              AND date3 >= date2 THEN date3
                         ELSE date1
                    END AS MostRecentDate
          FROM      data_table
        ) AS date_query 

Either of the two samples below will work:

The second is an add on to lassevk's answer.

SELECT
    MAX(date_columns) AS max_date
FROM
     (
        (
 SELECT   date1 AS date_columns
       SELECT
    FROM     data_table       date1 AS date_columns)
            FROMUNION
           ( SELECT  date2 AS data_tabledate_columns
        )
    FROM    UNIONdata_table
        (
  )
          SELECTUNION
             ( SELECT  date2date3 AS date_columns
            FROM
      data_table
          data_table)
        )
       AS UNIONdate_query
      

The second is an add-on to lassevk's answer.

SELECT  MAX(MostRecentDate)
       FROM    ( SELECT
     CASE WHEN date1 >= date2
        date3 AS date_columns
            FROM
           AND date1 >= date3 THEN data_tabledate1
        ) 
     ) AS date_query

SELECT
    MAX(MostRecentDate)
FROM
    (
     WHEN date2 >= SELECTdate1
            CASE
                WHEN date1 >= date2 AND date1date2 >= date3 THEN date1date2
                WHEN date2 >= date1 AND date2 >= date3 THEN date2
WHEN date3 >= date1
             WHEN date3 >= date1 AND date3 >= date2 THEN date3
                ELSE AND date3 >= date2 THEN date3
                         ELSE date1
        date1
            END AS MostRecentDate
        FROM
  FROM      data_table
    data_table
    ) AS date_query 

Either of the two samples below will work:

The second is an add on to lassevk's answer.

SELECT
    MAX(date_columns) AS max_date
FROM
     (
        (
             SELECT
                date1 AS date_columns
            FROM
                data_table
        )
        UNION
        (
            SELECT
                date2 AS date_columns
            FROM
                data_table
        )
        UNION
        (
            SELECT
                 date3 AS date_columns
            FROM
                data_table
        ) 
     ) AS date_query

SELECT
    MAX(MostRecentDate)
FROM
    (
        SELECT
            CASE
                WHEN date1 >= date2 AND date1 >= date3 THEN date1
                WHEN date2 >= date1 AND date2 >= date3 THEN date2
                WHEN date3 >= date1 AND date3 >= date2 THEN date3
                ELSE                                        date1
            END AS MostRecentDate
        FROM
            data_table
    ) AS date_query

Either of the two samples below will work:

SELECT  MAX(date_columns) AS max_date
FROM    ( (SELECT   date1 AS date_columns
           FROM     data_table         )
          UNION
          ( SELECT  date2 AS date_columns
            FROM    data_table
          )
          UNION
          ( SELECT  date3 AS date_columns
            FROM    data_table
          )
        ) AS date_query

The second is an add-on to lassevk's answer.

SELECT  MAX(MostRecentDate)
FROM    ( SELECT    CASE WHEN date1 >= date2
                              AND date1 >= date3 THEN date1
                         WHEN date2 >= date1
                              AND date2 >= date3 THEN date2
                         WHEN date3 >= date1
                              AND date3 >= date2 THEN date3
                         ELSE date1
                    END AS MostRecentDate
          FROM      data_table
        ) AS date_query 
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Either of the two samples below will work:

The second is an add on to lassevk's answer.

SELECT
    MAX(date_columns) AS max_date
FROM
    (
        (
            SELECT
                date1 AS date_columns
            FROM
                data_table
        )
        UNION
        (
            SELECT
                date2 AS date_columns
            FROM
                data_table
        )
        UNION
        (
            SELECT
                date3 AS date_columns
            FROM
                data_table
        ) 
    ) AS date_query

SELECT
    MAX(MostRecentDate)
FROM
    (
        SELECT
            CASE
                WHEN date1 >= date2 AND date1 >= date3 THEN date1
                WHEN date2 >= date1 AND date2 >= date3 THEN date2
                WHEN date3 >= date1 AND date3 >= date2 THEN date3
                ELSE                                        date1
            END AS MostRecentDate
        FROM
            data_table
    ) AS date_query