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Finding GCF and LCM with Venn Diagrams by St. Lawrence-Lewis BOCES

Grade Levels

Intermediate, 7th Grade


Students will hand in a completed Venn diagram finding the GCF and LCM of numbers they choose.


  • Review with students how to factor numbers using a factor tree.
  • Review how to fill in a Venn diagram. You can do up to 3 numbers. Start with two. Label each circle with one of the numbers. Explain that any factor shared will go in the overlapping area. To check their work, each circle will contain the prime factors of the number that they are factoring.
  • When they have completed a few factor trees correctly, give them two numbers that they need to find the GCF and LCM.
  • Once they have found the prime factors of each number help them fill in the Venn diagram.
  • Explain that the number(s) that appear in the center of the Venn diagram represent the GCF. To find the LCM they need to multiply all the numbers in the Venn diagram.


Usually takes two days of class time (42-minute class periods).


Pencil, Paper

  • Example of Venn Diagram.doc
  • Reflections and Feedback

    Most students liked using the Venn diagram method to find GCF and LCM.

    Related Resource

  • example of venn diagram
  • Description

    Students will learn to find the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) by using factor trees and a Venn diagram.

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