MIcompany Puzzle: Susanne's Cakes

For the annual Charity Market, Susanne has baked several cakes to sell. On the way someone bumps into her, so that all of the cakes fall on the floor and are no longer edible. Fortunately, the person who bumped into her offers to buy replacement cakes for her and he asks how many cakes there were. Susanne only knows that when she sorted the cakes into groups of three, she left two cakes. In groups of five she had four cakes left over and in groups of seven, six cakes remained.

What is the smallest number of cakes that Susanne can have baked?

Find out the answer in the article of next week: PhD Life, an article by Meindert Heres Hoogerkamp about his unusual curriculum!