Riddler Classic, Dec 13

2ab + 2ac + 2bc = abc
2ab = abc - 2ac - 2bc
    = (ab - 2a - 2b)*c
    = [(a-2)*(b-2)-4]*c
c = 2ab/[(a-2)*(b-2)-4]

WLoG, a<=b<=c
a>2
 a,  b, a-2, b-2, prod, -4, 2ab,  c
 3,  3,   1,   1,    1, -3,  18, -6
 3,  7,   1,   5,    5,  1,  42, 42
 3,  8,   1,   6,    6,  2,  48, 24
 3,  9,   1,   7,    7,  3,  54, 18
 3, 10,   1,   8,    8,  4,  60, 15
 3, 11,   1,   9,    9,  5,  66, 66/5
 3, 12,   1,  10,   10,  6,  72, 12
 4,  5,   2,   3,    6,  2,  40, 20
 4,  6,   2,   4,    8,  4,  48, 12
 4,  7,   2,   5,   10,  6,  56, 56/6
 4,  8,   2,   6,   12,  8,  64, 8
 5,  5,   3,   3,    9,  5,  50, 10
 5,  6,   3,   4,   12,  8,  60, 60/8
 5,  7,   3,   5,   15, 11,  70, 70/11
 6,  6,   4,   4,   16, 12,  72, 6

3*7*42 = 2*3^2*7^2 = 2*441 = 882
2*3*7 + 2*3*42 + 2*7*42 = 42+252+588 = 882

3*8*24 = 576
2*3*8 + 2*3*24 + 2*8*24 = 48+144+384 = 576

3*9*18 = 486
2*3*9 + 2*3*18 + 2*9*18 = 54+108+324 = 486

3*10*15 = 450
2*3*10 + 2*3*15 + 2*10*15 = 60+90+300 = 450

3*12*12 = 432
2*3*12 + 2*3*12 + 2*12*12 = 72+72+288 = 432

4*5*20 = 400
2*4*5 + 2*4*20 + 2*5*20 = 40+160+200 = 400

4*6*12 = 288
2*4*6 + 2*4*12 + 2*6*12 = 48+96+144 = 288

4*8*8 = 256
2*4*8 + 2*4*8 + 2*8*8 = 64+64+128 = 256

5*5*10 = 250
2*5*5 + 2*5*10 + 2*5*10 = 50+100+100 = 250

6*6*6 = 216
2*6*6 + 2*6*6 + 2*6*6 = 72+72+72 = 216