Theorem: Pandigital Numbers Divisible by All Integers up to 18

The following pandigital integers are divisible by all the positive integers up to $18$:
:$2 \, 438 \, 195 \, 760$
:$3 \, 785 \, 942 \, 160$
:$4 \, 753 \, 869 \, 120$
:$4 \, 876 \, 391 \, 520$

Proof:
{{begin-eqn}}
{{eqn | l = 2 \, 438 \, 195 \, 760
      | r = 2 \times 1 \, 219 \, 097 \, 880
}}
{{eqn | r = 3 \times 812 \, 731 \, 920}}
{{eqn | r = 4 \times 609 \, 548 \, 940}}
{{eqn | r = 5 \times 487 \, 639 \, 152}}
{{eqn | r = 6 \times 406 \, 365 \, 960}}
{{eqn | r = 7 \times 348 \, 313 \, 680}}
{{eqn | r = 8 \times 304 \, 774 \, 470}}
{{eqn | r = 9 \times 270 \, 910 \, 640}}
{{eqn | r = 10 \times 243 \, 819 \, 576}}
{{eqn | r = 11 \times 221 \, 654 \, 160}}
{{eqn | r = 12 \times 203 \, 182 \, 980}}
{{eqn | r = 13 \times 187 \, 553 \, 520}}
{{eqn | r = 14 \times 174 \, 156 \, 840}}
{{eqn | r = 15 \times 162 \, 546 \, 384}}
{{eqn | r = 16 \times 152 \, 387 \, 235}}
{{eqn | r = 17 \times 143 \, 423 \, 280}}
{{eqn | r = 18 \times 135 \, 553 \, 320}}
{{end-eqn}}
{{begin-eqn}}
{{eqn | l = 3 \, 785 \, 942 \, 160
      | r = 2 \times 1 \, 892 \, 971 \, 080
}}
{{eqn | r = 3 \times 1 \, 261 \, 980 \, 720}}
{{eqn | r = 4 \times 946 \, 485 \, 540}}
{{eqn | r = 5 \times 757 \, 188 \, 432}}
{{eqn | r = 6 \times 630 \, 990 \, 360}}
{{eqn | r = 7 \times 540 \, 848 \, 880}}
{{eqn | r = 8 \times 473 \, 242 \, 770}}
{{eqn | r = 9 \times 420 \, 660 \, 240}}
{{eqn | r = 10 \times 378 \, 594 \, 216}}
{{eqn | r = 11 \times 344 \, 176 \, 560}}
{{eqn | r = 12 \times 315 \, 495 \, 180}}
{{eqn | r = 13 \times 291 \, 226 \, 320}}
{{eqn | r = 14 \times 270 \, 424 \, 440}}
{{eqn | r = 15 \times 252 \, 396 \, 144}}
{{eqn | r = 16 \times 236 \, 621 \, 385}}
{{eqn | r = 17 \times 222 \, 702 \, 480}}
{{eqn | r = 18 \times 210 \, 330 \, 120}}
{{end-eqn}}
{{begin-eqn}}
{{eqn | l = 4 \, 753 \, 869 \, 120
      | r = 2 \times 2 \, 376 \, 934 \, 560
}}
{{eqn | r = 3 \times 1 \, 584 \, 623 \, 040}}
{{eqn | r = 4 \times 1 \, 188 \, 467 \, 280}}
{{eqn | r = 5 \times 950 \, 773 \, 824}}
{{eqn | r = 6 \times 792 \, 311 \, 520}}
{{eqn | r = 7 \times 679 \, 124 \, 160}}
{{eqn | r = 8 \times 594 \, 233 \, 640}}
{{eqn | r = 9 \times 528 \, 207 \, 680}}
{{eqn | r = 10 \times 475 \, 386 \, 912}}
{{eqn | r = 11 \times 432 \, 169 \, 920}}
{{eqn | r = 12 \times 396 \, 155 \, 760}}
{{eqn | r = 13 \times 365 \, 682 \, 240}}
{{eqn | r = 14 \times 339 \, 562 \, 080}}
{{eqn | r = 15 \times 316 \, 924 \, 608}}
{{eqn | r = 16 \times 297 \, 116 \, 820}}
{{eqn | r = 17 \times 279 \, 639 \, 360}}
{{eqn | r = 18 \times 264 \, 103 \, 840}}
{{end-eqn}}
{{begin-eqn}}
{{eqn | l = 4 \, 876 \, 391 \, 520
      | r = 2 \times 2 \, 438 \, 195 \, 760
      | c = see above
}}
{{eqn | r = 3 \times 1 \, 625 \, 463 \, 840}}
{{eqn | r = 4 \times 1 \, 210 \, 097 \, 880}}
{{eqn | r = 5 \times 975 \, 278 \, 304}}
{{eqn | r = 6 \times 812 \, 731 \, 920}}
{{eqn | r = 7 \times 696 \, 627 \, 360}}
{{eqn | r = 8 \times 609 \, 548 \, 940}}
{{eqn | r = 9 \times 541 \, 821 \, 280}}
{{eqn | r = 10 \times 487 \, 639 \, 152}}
{{eqn | r = 11 \times 443 \, 308 \, 320}}
{{eqn | r = 12 \times 406 \, 365 \, 960}}
{{eqn | r = 13 \times 375 \, 107 \, 040}}
{{eqn | r = 14 \times 348 \, 313 \, 680}}
{{eqn | r = 15 \times 325 \, 092 \, 768}}
{{eqn | r = 16 \times 304 \, 774 \, 470}}
{{eqn | r = 17 \times 286 \, 846 \, 560}}
{{eqn | r = 18 \times 270 \, 910 \, 640}}
{{end-eqn}}
{{ProofWanted|Prove that these are the only ones}}