Greatest Common Divisor and Least Common Multiple

Learning Objectives¹

•To understand and to be able to apply the definition of the greatest common divisor
(GCD) of two integers .
•To be able to find the GCD of two integers using the Colored Rods Method , Intersection-
of- Sets Method , the Prime Factorization Method , and the Euclidean Algorithm.
•To understand and to be able to apply the definition of the least common multiple
( LCM ) of two integers .
•To be able to find the LCM of two integers using the Colored Rods Method, Division-
by- Primes Method , the Prime Factorization Method , and the Euclidean Algorithm.

Testing Your Knowledge

1. Find the GCD of 6 and 8 using the Colored Rods Method .

2. Find the LCM of 3 and 4 using the Colored Rods Method.

3. Find the GCD of 132 and 504 using the Prime Factorization Method .

4. Find the GCD of 132 and 504 using the Euclidean Algorithm.

5. Find the LCM of 132 and 504 using the Prime Factorization Method.

6. Find the LCM of 132 and 504 using the Euclidean Algorithm.

¹Section 4.5 in R. Billstein, S Libeskind, and J. Lott. A Problem Solving Approach to Mathematics for
Elementary School Teachers, ninth edition. Addison Wesley , Boston, 2007