Education Technology

GCD and LCM

Published on 06/09/2008

Activity Overview

In this activity students use the Computer Algebra System CAS tool to compute greatest common divisor (GCD) and least common multiple (LCM) of numbers and expressions.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 10 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Factorize two large numbers and find their GCD
  • Understand that if a number is the GCD of two or more numbers, then the quotients of the given numbers and the GCD do not have any prime factors in common
  • Study the proof for the above statement
  • Determine the GCD of two large expressions
  • Discover the concept of a nested function and use it to calculate the GCD for three or more numbers
  • Find GCD of non-integer numbers and interpret the outcomes
  • Use the concept of GCD to solve problems
  • Repeat the procedure to compute the LCM of numbers/expressions
  • Find the relationship between the LCM of two expressions, the expressions themselves, and their GCD
  • After the Activity

    Students complete the exercises listed on the activity pages.

    Review student results.

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary