Lesson objective: Understand that a common multiple of a set of numbers has each number in the set as a factor. Furthermore, the list of factors of the common multiple also includes every factor of the numbers in the original set.

Students bring prior knowledge of factors and multiples from Grade 4 (4.OA.4). This prior knowledge is extended to common multiples and common factors of given numbers as students find the least common multiple and greatest common factor of given sets of numbers. A conceptual challenge students may encounter is confusing the meaning of factors and multiples.

The concept is developed through work with lists of factors and multiples, which allow students to see patterns formed and to find commonalities. This work helps students deepen their understanding of operations because they use factors and multiples to find the GCF and LCM and explore the multiplicative relationships formed between the factors and multiples of a given set of numbers.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they look at the relationships between factors and multiples in a given set of numbers. Students will understand that a multiple of a number means that it is a given number multiplied by a whole number. For example, 24 isn’t just a multiple of 8, it is three 8’s.

**Key vocabulary:**

- factor
- greatest common factor
- least common multiple
- multiple
- set