LCM and GCF-Listing and Venn Diagram

Today is class we took a quiz.  After I graded the quiz and went over the quiz with them, we began work on least common multiple.  To find least common multiples, we take each number and multiply it by 1, 2, 3, etc., until we find a multiple that they have in common.  For example, 20 and 30 have common multiples of 60, 120, and 180, with 60 being the least (or lowest).  Multiples are also known as products, and must always be equal to or larger than the number itself.  See the example below.

We have been finding factors, but we haven't compared the factors of two numbers.  Below we look at 20 and 30 again.  I used a Venn Diagram to organize my work.  The factors of 20 go into the circle under 20 and they are 1, 2, 4, 5, 10, and 20.  The factors for 30 go into the circle under 30 and they are 1, 2, 3, 5, 6, 10, 15, and 30.  In the area where the circles overlap we put the factors they have in common.  1, 2, 5, and 10 are all the common factors of 20 and 30.  When we find the greatest common factor, we use the largest one inside the overlap of the circles.  In this case, the greatest common factor of 20 and 30 is 10.  See the example below.

This is what is covered in the homework.  For 2, 4, 6, and 8, follow the first example (Least Common Multiple) for 16, 18, 20, and 22 follow the second example (Greatest Common Factor)

Below is a picture of the listing method for GCF.