Question 549903
If you had 2 children less, you could put them into groups of 3,4 or 6, without any children left over. That would be possible if the number of children were a multiple of 3, 4, and 6. The least of all the multiples of 3,4, and 6 is 12, the minimum common multiple of those three numbers.
The least number of children you could have, if you always have 2 left over, is 14, 2 more than 12.