Products with embedded indices

Éric Angelini did a "smallest multiplication" bit yesterday that I felt was worth extending.

     0 0 = 0 * 1
     1 10 = 2 * 5
     2 12 = 3 * 4
     3 132 = 6 * 22
     4 84 = 7 * 12
     5 152 = 8 * 19
     6 126 = 9 * 14
     7 170 = 10 * 17
     8 198 = 11 * 18
     9 195 = 13 * 15
    10 1008 = 16 * 63
    11 1100 = 20 * 55
    12 1218 = 21 * 58
    13 713 = 23 * 31
    14 1416 = 24 * 59
    15 1150 = 25 * 46
    16 1612 = 26 * 62
    17 1728 = 27 * 64
    18 1820 = 28 * 65
    19 1914 = 29 * 66
    20 1020 = 30 * 34
    21 1216 = 32 * 38
    22 1221 = 33 * 37
    23 2345 = 35 * 67
    24 2448 = 36 * 68
    25 2925 = 39 * 75
    26 12600 = 40 * 315
    27 1927 = 41 * 47
    28 2898 = 42 * 69
   ...

The column of indices on the far left is shown embedded (in bold) in their adjacent products. The constraint on the multiplier and multiplicand is that they must be distinct nonnegative integers with the multiplier the smallest such not yet used and the multiplicand the smallest such that yields the embedded index. A chart extending the products is here.