Factoring and Lowest Common Multiple - Practice

This math unit starts with teaching students the fundamentals of prime factorization, enabling them to break down numbers into their prime components using factor trees. As students advance, they explore Venn diagrams to grasp the relationship between different sets of numbers, primarily focusing on identifying common and distinct factors. The unit progresses to more complex applications by teaching how to utilize these factorizations to find the lowest common multiple (LCM) of two and eventually three numbers. This skill is fundamental in solving problems involving the LCM in both numerical and variable formats, enhancing students' understanding of divisibility, multiples, and their practical applications in different scenarios. Through a repetitive, yet increasingly challenging set of exercises, students strengthen their factoring skills and apply these in diverse contexts, including populating Venn diagrams correctly and determining multiplicity from algebraic expressions. This structured progression is vital for mastering the essentials of number theory related to factors and multiples.