I believe it can easily be seen that a number of form xy or abc where
xy and abc are not ordered in ascending order
cannot yield a solution hence:

ruby -e 'p (3...7).map{|x|([*3..7]-[x]).map{|y| three=[*3..7]-[x,y];
two=[x,y]; [three.join.to_s.to_i * two.join.to_s.to_i, three,
two]}}.sort.first.sort.first'
[16345, [4, 6, 7], [3, 5]]

HTH
Robert

-- 
C'est vٔitablement utile puisque c'est joli.

Antoine de Saint Exupٔy