🏛️Euclid's algorithm for GCD, from 300 BC, is one of the oldest algorithms still in use today
🔐RSA encryption uses GCD to verify that public and private keys are properly generated
🎵Music theory uses LCM to find when polyrhythms align - like 3 against 4 beats
⚙️Gear ratios in machines use GCD to simplify tooth counts for efficient power transfer
📅Calendar calculations use LCM - leap years repeat every LCM(4, 100, 400) = 400 years
🧬DNA sequence alignment algorithms use GCD-based methods for pattern matching
🎲If GCD of two numbers is 1, they're 'coprime' - only 1 divides both evenly
🔢For any two numbers a and b: a × b = GCD(a,b) × LCM(a,b) - always!