When just a rule is given by an instructor, often times, students get lost in the mathematical process. I have found that utilizing a visual can achieve an understanding of a concept better than just a rule. A Venn Diagram is such a visual and helps students to follow the process and understand the connection and relationship between each step of finding the GCF and LCM.

It's important to always begin with the definitions for the

words factor, greatest common factor and least common multiple. If a student doesn't know the vocabulary, they can't do the work! I continue by explaining and illustrating what a factor tree is (on your left) and how to construct and use a Venn Diagram as a graphic organizer.

Let's suppose we have the algebraic terms of

**75**and*xy***45**. I have the students construct factor trees for each of the numbers as illustrated on the left.*xyz*
Then all the common factors are placed in the intersection of the two circles. In this case, it would be the

The students then put the remaining factors and variables in the correct big circle. Five and three would go in the left hand circle and the three

The intersection is the GCF; so, the GCF for 75xy and 40xyz is

**5**and the*.***xy**The students then put the remaining factors and variables in the correct big circle. Five and three would go in the left hand circle and the three

**2’s**and the*would be placed in the right hand circle.***z**The intersection is the GCF; so, the GCF for 75xy and 40xyz is

**5xy**. To find the LCM, multiply the number(s) in the first big circle by the GCF (numbers in the intersection) times the number (s) in the second big circle.**5 × 3 × GCF × 2 × 2 × 2 × z = 15 × 5xy × 8z = 240. The LCM is 600xyz.**

Free Item |

^{2}y

^{3 }+ 9xy

^{2}. Using a Venn Diagram is also an effective and valuable tool when teaching how to reduce fractions.

Are you interested in finding out more about this method? Then download my newest

**resource entitled:**

__free__**Algebraic Terms and Fractions - Finding the Greatest Common Factor and the Lowest Common Multiple Using a Venn Diagram.**