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

[MatheMatt]

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.

 

[berkeman]

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.

 

[VeeEight]

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.