According to Harel's Necessity Principle (1998) “students are most likely to learn when they see a need for what we intend to teach them, where by need is meant intellectual need, not social or economic need” (p. 501). Intellectual need for a particular mathematical concept is an internal drive experienced by a learner to solve a problem. In this paper, I discuss how tasks can be designed to provoke the intellectual need for two mathematical ideas, prime factorization and lowest common multiple.