1. An egg vendor was delivering a shipment of eggs and had an accident. All the eggs he had were broken. He could not remember how many eggs he had to deliver. However, he remembered that when he had tried to pack the eggs in packages of 2, 3, 4, 5, or 6, he had one egg left over. Nonetheless, when he packed them into packages of 7, he had no left over. What is the smallest number of eggs he could have shipped in the shipment?

2. Eleven consecutive integers add up to 418. Find the largest among the integers.