Append three columns in LibreOffice

Create a new LibreOffice Base file (File -> New -> Database). Press Next and then "No, do not register the database." Then press Finish and save the file.

Back in the spreadsheet, select cells A1 through C4. Drag this selection over to the LO Base window where it says Tables. (It may help to move the windows so that Base is on one side of the screen and Calc is on the other side). Then check the boxes "Use first line as column names" and "Create new field as primary key," and press Create.

The resulting table should look like this.

Next, go to the Queries area and press "Create Query in SQL view." Enter the following query.

select A from "Table1"
union select B from "Table1"
union select C from "Table1"

Base complains about this syntax, so go to Edit -> Run SQL command directly to make it stop complaining. Now save and close the query as "Query1".

Finally, drag and drop "Query1" to column E in the spreadsheet.