pair of positive integer

find all pairs of positive integer a,b,c which satisfy (1+1/a)(1+1/b)(1+1/c) = 3

a=<b=<c
==>3=(1+1/a)(1+1/b)(1+1/c) =<(1+1/a)^3
==> 1+1/a>=3^(1/3)
==> a=<1/(3^(1/3)-1)<3
==> a=<2

si a=1
3/2=(1+1/b)(1+1/c)=<(1+1/b)²
==> b=<1/((3/2)^(1/2)-1)<5
==> b=<4
si b=1, 1+1/c=3/4 >1 impossible
si b=2, ...
si b=3,..
si b=4, ...

si a=2
....