Amount of rectangles is equal to the number of divisiors of tiles count wich are no more than Square_Root(tiles count). So the part of code solving this problem may be the following:

  For L:=1 To 10000-K Do Begin
    DivisiorsCount:=1;
    For J:=2 To Trunc(Sqrt(L)) Do If L Mod J=0 Then
      Inc(DivisiorsCount);

    If DivisiorsCount=M Then Begin
      DivisiorsCount2:=1;
      For J:=2 To Trunc(Sqrt(L+K)) Do If (L+K) Mod J=0 Then
        Inc(DivisiorsCount2);

      If DivisiorsCount2=N Then Begin
        SoulutionExists:=True;
        Break;
      End;
    End;
  End;

You should output L+K if SolutionExists, 0 - otherwise.