ABSTRACT
Many students are challenged when it comes to determining the common denominators or least common multiples (LCMs) for rational expressions with variables. This is partially due to their discomfort with fractions in general and because many students have been told to cross-multiply. Students need to develop conceptual understanding of the fact that the least common denominator is the smallest shared multiple of both values in the denominators. On the Cartesian coordinate plane, the LCM is the first time both rational expressions share the same x-value on the grid. For factor lattices, the LCM is the first vertex at which the two operators intersect. Calculating the LCM or greatest common factor is challenging when working with numbers but much more difficult when working with variables and exponents.
