Start by giving your students this challenge. After that, students will learn how to determine whether two numbers are relatively prime, also known as coprime. They'll also learn how two numbers being relatively prime relates to the GCD, LCM, and the reducibility of fractions. As an example problem, are \(21\) and \(55\) relatively prime? Students can practice here. As another example problem, what's the GCD of \(21\) and \(55?\) LCM? Watch this video for a lesson. Students can practice this skill here. Conclude by leading this investigation.
Note: Numbers being relatively prime, or coprime, is not covered by the Common Core, but I think it should be.