LCM and GCD Calculator to Find Least Common Mult...
Calculate the LCM and GCD of two or more integers instantly. Understand prime factorization methods, the Euclidean algorithm, and real-world applications.
What are LCM and GCD?
The Greatest Common Divisor (GCD) is the largest integer that divides two numbers without remainder. The Least Common Multiple (LCM) is the smallest positive integer divisible by both. They are related by: LCM × GCD = a × b. Both appear in fractions, modular arithmetic, and scheduling problems.
🔢 LCM & GCD Calculator
Use our free calculator for instant, accurate results.
📐 Formula
GCD via Euclidean: GCD(a,b) = GCD(b, a mod b)
Repeat until remainder = 0. LCM(a,b) = (a × b) / GCD(a,b). Works for multiple numbers too by applying iteratively.
📝 Worked Example
GCD(48, 18):
48 = 2×18 + 12 → GCD(18,12)
18 = 1×12 + 6 → GCD(12,6)
12 = 2×6 + 0 → GCD = 6
LCM(48,18) = 48×18/6 = 144
📝 How to Use the Calculator
❓ FAQ
What is GCD used for in real life?
Simplifying fractions (divide numerator and denominator by GCD), evenly distributing items into groups, and cryptography (RSA algorithm).
When is LCM useful?
Adding fractions (finding common denominator), synchronizing periodic events (gear cycles, traffic lights), and solving Diophantine equations.
Veer Kumavat
Founder & AuthorVeer is a 14-year-old student from Nashik, Maharashtra, who built SciFi Calculators to help students worldwide master STEM subjects. He is passionate about making complex science and math problems accessible through intuitive digital tools.