Please help me solve the following problems following and using Polya's Four Step Method and employing the different strategies. Thank you!

(#1 - Understand the problem, #2 - Devise a plan (translate), #3 - Carry out the plan (solve), and #4 - Look back (check and interpret).

PROBLEM:

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?

(Source: Alfred S. Posamentier's Problem-solving strategies for efficient and elegant solutions)