# Activities

• • • ##### Subject Area

• Math: Math General: General

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

## GCD and LCM

#### 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.

• 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