A street vendor selling electronic gadgets was robbed of all possessions. When reporting the matter to the police, the vendor could not recall the number of gadgets but stated that when dividing the total in lots of size 2, 3, 4, 5, or 6, there was always one gadget left over, but no remainder when the total was divided into lots of size 7. The police was interested in the smallest number of gadgets the vendor has had prior to robbery. Use ILP to determine the total number of gadgets per the police request.