ELEMENT OF MAXIMUM POSSIBLE ORDER

- Not applicable to super cubes or cubes with permuted true centers
- 6x6x6 and 7x7x7 cubes: no published solution found yet
- The LCM (Least Common Multiple) is given for each orbit first, then for the complete cube

3x3x3 Cube (David Singmaster):
- twisted corner 3-cycles and 5-cycles: 3x(3x5) = (9x5)
- twisted edge 2-cycles and 7-cycles: 2x(2x7) = (4x7)
- LCM: (9x5)x(4x7) = 1260
- element of maximum permutation order: 1260
- algorithm (5 moves): B2 R' F D' F

4x4x4 Cube (Tony Forbes)
- twisted corner 3-cycles and 5-cycles: 3x(3x5) = (9x5)
- edge 7-cycle and 17-cycle: (7x17)
- center 11-cycle and 13-cycle: (11x13)
- LCM: (9x5)x(7x17)x(11x13) = 765765
- element of maximum permutation order: 765765
- algorithm (5 moves): NF NU2 B' TD2 TU

5x5x5 Cube (Tony Forbes)
- twisted corner 3-cycles and 5-cycles: 3x(3x5) = (9x5)
- twisted edge 4-cycle and 8-cycle: 2x(8)
- edge 7-cycle and 17-cycle: (7x17)
- center 11-cycle, 13-cycle and 23-cycle: (11x13x23)
- LCM: (9x5)x(2x8)x(7x17)x(11x13x23) = 281801520
- element of maximum permutation order: 281801520
- algorithm (11 moves): NF NR' L2 F2 B U2 ND NL R F U