It's So Elegant! 😍 Prove gcd(a,b)*lcm(a,b)=a*b with the GCD is a Linear Combination Theorem

An elegant proof that a*b is the product of gcd(a,b) and lcm(a,b) in number theory can be done using the fact that gcd(a,b) = a*s + b*t for some integers s and t. "Friendly Introduction to Number Theory": https://amzn.to/3Ixo9Lq. This is the "GCD is a Linear Combination Theorem". 🔴 Number Theory Examples and Proofs:    • Number Theory Examples and Proofs   🔴 Ultimate AP Calculus AB Review:    • Ultimate AP Calculus AB Review   🔴 Abstract Algebra Course Lectures playlist:    • Abstract (Modern) Algebra Course Lectures   #numbertheory #number #numbers Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ (0:00) Introduction (0:24) Example: a = 30, b = 36 (2:19) Proof using GCD is a linear combination AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.