Proving GCD(a,b)*LCM(a,b) = ab

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SUMMARY

The discussion centers on proving the mathematical identity GCD(a,b) * LCM(a,b) = a * b. Participants emphasize the importance of understanding the definitions of GCD (Greatest Common Divisor) and LCM (Least Common Multiple) as foundational steps in the proof. They suggest rearranging the equations derived from these definitions to clarify the relationship between GCD, LCM, and the product of a and b. The consensus is that a structured approach using definitions will lead to a successful proof.

PREREQUISITES
  • Understanding of GCD (Greatest Common Divisor)
  • Understanding of LCM (Least Common Multiple)
  • Basic algebraic manipulation skills
  • Familiarity with mathematical proofs
NEXT STEPS
  • Study the formal definitions of GCD and LCM in number theory
  • Practice algebraic rearrangement techniques
  • Explore examples of GCD and LCM calculations
  • Learn about properties of GCD and LCM in relation to prime factorization
USEFUL FOR

Students in mathematics, particularly those studying number theory or foundational mathematics, as well as educators seeking to reinforce concepts of GCD and LCM in their curriculum.

MatheMatt
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I need help in my Foundations of Mathematics class. I am supposed to prove that the GCD(a,b) multiplied by the LCM(a,b) is equal to ab(a multiplied by b). If anyone has any clue how to prove this, I would be grateful for your help.
 
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MatheMatt said:
I need help in my Foundations of Mathematics class. I am supposed to prove that the GCD(a,b) multiplied by the LCM(a,b) is equal to ab(a multiplied by b). If anyone has any clue how to prove this, I would be grateful for your help.

Start by writing down the definitions of the GCD and the LCM. What are the mathematical definitions for each? From the definitions, are you able to see some approaches to proving the equation?

Welcome to the PF, BTW. We do not give out answers here to homework/coursework questions, but we can provide hints and tutorial help, as long as you show your work and do the bulk of the work on the problem.
 
Rearranging the equations would probably help you see things clearer (ie, rearranging so you get something like gcd(a,b) = something or lcm(a,b) = something). Do what the above poster said, write down what gcd and lcm means and then use those definitions to show that your equation is satisfied.
 

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