### Multiplication magic square

Why adding numbers to get the magic sum? You get the magic sum if you multiply the numbers in the multiplication magic square.

3x3 multiplication magic square

 216 216 216 216 216 216 18 1 12 216 4 6 9 216 3 36 2

Source:  Sayles, 1913

4x4 multiplication magic square (with smallest possible digits)

 5040 5040 5040 5040 5040 5040 5040 1 15 24 14 5040 12 28 3 5 5040 21 6 10 4 5040 20 2 7 18

Source:  Sayles

5x5 multiplication magic square

 362880 362880 362880 362880 362880 362880 362880 362880 1 15 42 16 36 362880 14 32 9 3 30 362880 27 6 10 28 8 362880 20 7 24 54 2 362880 48 18 4 5 21

Source:  Marián Trenkler, 19 januari 2001

6x6 panmagic and 2x2 & 3x3 compact multplication magic square

 729 16 23328 1 11664 32 576 324 18 5184 36 162 3 3888 96 243 48 7776 46656 4 1458 64 2916 2 9 1296 288 81 144 2592 192 972 6 15552 12 486

Source:  W.S. Andrews, magic squares and cubes, Dover, publ., 1960, p. 292

8x8 Franklin panmagic multiplication magic square

 1 1080 42 1260 3 360 14 3780 378 140 9 120 126 420 27 40 180 6 7560 7 540 2 2520 21 840 63 20 54 280 189 60 18 36 30 1512 35 108 10 504 105 168 315 4 270 56 945 12 90 5 216 210 252 15 72 70 756 1890 28 45 24 630 84 135 8

Source:  Christian Boyer, 2006

8x8 Multiplication ánd addition magic square

 162 207 51 26 133 120 116 25 105 152 100 29 138 243 39 34 92 27 91 136 45 38 150 261 57 30 174 225 108 23 119 104 58 75 171 90 17 52 216 161 13 68 184 189 50 87 135 114 200 203 15 76 117 102 46 81 153 78 54 69 232 175 19 60

Source:  Dénes en Keedwell

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