Use the relationship you described (or the one given in the solutions to Homework 2) to prove Theorem 7.5 from the textbook. Or equivalently, to prove the following: gcd(a, b) · lcm(a, b) = a · b, for any positive integers a, and b. Note: You can not prove that a statement is true in general by showing it is true for some example numbers. You must use variables and full sentences to prove the above statement is true for any positive integers a and b.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 40E
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Use the relationship you described (or the one given in the solutions to Homework 2) to prove Theorem 7.5 from the textbook. Or equivalently, to prove the following:

gcd(a, b) · lcm(a, b) = a · b,

for any positive integers a, and b. Note: You can not prove that a statement is true in general by showing it is true for some example numbers. You must use variables and full sentences to prove the above statement is true for any positive integers a and b.

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