Lesson objective: Generate a rule for the relationship among the product, GCF and LCM of two given numbers.

This lesson provides an opportunity for students to apply their knowledge and understanding of factors and multiples to a mathematical situation. Students are asked to generate the product, GCF and LCM for pairs of numbers and create a general rule that applies to the relationship among the product, GCF and LCM.

Key Concept students will use:

- 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.

Skills students will use:

- multiplying whole numbers (Grade 4, Unit 2)
- finding the greatest common factor of two given numbers
- finding the least common multiple

Students engage in Mathematical Practice 8 (Look for and express regularity in repeated reasoning) as they find the relationship among the product, GCF and LCM of two given numbers. Students will use a table format to help structure their work to see the relationship.

**Key vocabulary: **

- greatest common factor
- least common multiple
- product

**Special materials needed:**

- 12-sided dice or spinners or random number generator (1-12)