When programs are created as stand alone programs, they often have a particular character set at the beginning. Fanuc have the O character, plus a program number, Okuma can have MIN, and so on. If your control uses such characters, you need to remove these from the head of the two programs being appended to the first. Failing to doe this with a Fanuc control will result in the combined programs being split back into the original three by the control when the program is uploaded. Also, the M30 or M02, along with any control characters, such as "%", need to be deleted from the 1st and 2nd programs.
Its also usual for a safety line to appear at the head of a stand alone program, such as:
N1 G00 G17 G21 G40 G49 G80
When the two other programs are appended to the first, the above line appearing at the head of these two programs will be superfluous, but will not affect the running of the programs in any way. Accordingly, it is quite optional whether these extra blocks are deleted or not.