An egg vendor broke all the eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages...

An egg vendor broke all the eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages of 2, 3, 4, 5, and 6 he had one left over each time. When he packed them into packages of 7, he had none left over. What is the smallest number of eggs he could have had in shipment?