# Math Building Blocks: Chapter 4GCFs and LCMs

Task: Figure out how the lower diagram in each box is determined by the upper two diagrams. Explain in terms of numbers. Create your own examples.
Learning goals: Use prime factorizations to find the greatest common factor of two numbers.

Task: Figure out how the lower diagram in each box is determined by the upper two diagrams. Explain in terms of numbers. Create your own examples.
Learning goals: Use Math Building Blocks to recognize least common multiples of two numbers.

Task: Describe the processes for obtaining the final diagrams on the left and right from the two diagrams on the top.
Learning goals: Use prime factorizations to understand a strategy for finding the least common multiple of two numbers.

Task: Describe the processes for obtaining the final diagrams on the left and right from the two diagrams on the top.
Learning goals: Use prime factorizations to understand a second strategy for finding the least common multiple of two numbers.

Task: Describe the process for obtaining the final diagram on the lower right from the two diagrams on the top left.
Learning goals: Use prime factorizations to understand a third strategy for finding the least common multiple of two numbers.

Task: Discover and describe an important relationship between the top two diagrams and the bottom two diagrams in each box. Relate your conclusions to your learning from 4-2, 4-3, 4-4, and 4-5.
Learning goals: Discover, describe, and justify the relationship between the GCF and LCM of two numbers.

Tasks: Complete the image according the pattern in 4-6. Compare and contrast your results to 4-6.
Learning goals: Determine which patterns and strategies for GCFs and LCMs generalize to the case of more than two numbers.