Products containing the same digits

Question

I am looking for $d_1$ and $d_2$, where $d_1$ is a two digit integer and $d_2$ is a three digit integer, such that $d_1\cdot d_2$ is a product that contains the exact same digits as $d_1$ and $d_2$.

For example when $d_1$ is a single digit integer ($6$) and $d_2$ is a two digit integer ($21$) their product is $126$ (same digits as $6$ and $21$).

Many years ago wrote a program in BASIC and found a two digit number and and a three digit number whose product contained the same five digits as $d_1$ and $d_2$, but I have forgotten the numbers.

Answer 1

This simple Mathematica code

Do[If[Sort[Join[IntegerDigits[m], IntegerDigits[n]]] == 
   Sort[IntegerDigits[m*n]], 
  Print[m, " x ", n, " = ", m*n]], {m, 10, 99}, {n, 100, 999}]

gives the desired output:

14 × 926 = 12964

15 × 705 = 10575

15 × 930 = 13950

21 × 501 = 10521

21 × 600 = 12600

21 × 870 = 18270

21 × 906 = 19026

21 × 915 = 19215

24 × 651 = 15624

26 × 401 = 10426

27 × 810 = 21870

30 × 501 = 15030

30 × 510 = 15300

32 × 926 = 29632

35 × 401 = 14035

35 × 410 = 14350

35 × 725 = 25375

36 × 936 = 33696

41 × 323 = 13243

41 × 350 = 14350

42 × 678 = 28476

47 × 371 = 17437

47 × 542 = 25474

50 × 251 = 12550

51 × 201 = 10251

51 × 246 = 12546

51 × 300 = 15300

53 × 635 = 33655

54 × 846 = 45684

57 × 834 = 47538

59 × 845 = 49855

60 × 201 = 12060

60 × 210 = 12600

63 × 585 = 36855

63 × 855 = 53865

65 × 281 = 18265

65 × 641 = 41665

65 × 704 = 45760

65 × 875 = 56875

65 × 983 = 63895

68 × 926 = 62968

72 × 936 = 67392

75 × 231 = 17325

75 × 906 = 67950

78 × 624 = 48672

80 × 473 = 37840

80 × 860 = 68800

81 × 225 = 18225

81 × 270 = 21870

84 × 141 = 11844

84 × 546 = 45864

86 × 251 = 21586

86 × 800 = 68800

87 × 210 = 18270

87 × 435 = 37845

89 × 482 = 42898

90 × 351 = 31590

93 × 150 = 13950