不妨设a≤b≤c,则有abc=2(a+b+c)≤2(c+c+c)=6c
所以有:1≤ab≤6,ab=1,即a=b=1,显然无解,
ab=2即a=1,b=2,显然无解,
ab=3即a=1,b=3,3c=2(4+c),c=8,(138)
ab=4=1×4=2×2,a=1,b=4,c=5,(145)
a=2,b=2,c=4,(224)
ab=5,a=1,b=5,c=4舍去(a≤b≤c)
ab=6=1×6=2×3,c无正整数解,
因为abc等价(145)145,154,415,451,541,514,6对;
(138)138,183,381,318,813,831,6对;
(224)224242422,3对,
故6+6+3=15组.
故选:D.