I have one feasible solution, not sure if it is optimal. You can find others for a check along the same lines.
C=4, 3 factors: 1,2,4
B=6, 4 factors: 1,2,3,6
A=12,6 factors: 1,2,3,4,6,12
N=72,12 factors: 1,2,3,4,6,8,9,12,18,24,36,72
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