GCD & LCM Calculator
Verified Calculation Engine
The online GCD & LCM Calculator helps you calculate instantly and solve problems related to Number Theory. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Calculate Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more numbers
GCD: Euclidean Algorithm, LCM: (a × b) / GCD(a, b)
GCD is calculated using Euclidean algorithm, LCM uses the relationship LCM(a,b) = (a × b) / GCD(a,b)
- Inputs are treated as integers for GCD/LCM semantics.
- For two numbers, LCM uses |a×b|/GCD(a,b).
Inputs
Results
Worked Examples
Example 1: GCD and LCM of 12 and 18
Find GCD and LCM of 12 and 18
- a: 12
- b: 18
- gcd: 6
- lcm: 36
Example 2: GCD and LCM of 24 and 36
Find GCD and LCM of 24 and 36
- a: 24
- b: 36
- gcd: 12
- lcm: 72
About this calculator
Overview
This calculator finds the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two integers (optional third input when provided by the form).
When to use
Use it for fraction simplification, scheduling/cycles, and number-theory homework where GCD or LCM is required.
Inputs explained
- Two positive integers (and an optional third when the form exposes it).
Formula / method
GCD uses the Euclidean algorithm. For two integers, LCM(a, b) = |a × b| / GCD(a, b) (with care for overflow in large products).
Worked example
Example: a = 12, b = 18 → GCD = 6, LCM = 36 because 12×18 / 6 = 36.
Interpreting results
GCD is the largest positive integer dividing both inputs. LCM is the smallest positive integer that is a multiple of both.
Assumptions
- Inputs are treated as integers for GCD/LCM semantics.
- Results follow the Euclidean / product–GCD relationship for two numbers.
Limitations
- Very large intermediates may be limited by numeric precision in the runtime.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
GCD uses the Euclidean algorithm. For two integers, LCM(a, b) = |a × b| / GCD(a, b) (with care for overflow in large products).
Example Calculation
Example: a = 12, b = 18 → GCD = 6, LCM = 36 because 12×18 / 6 = 36.
Frequently Asked Questions
What is GCD & LCM Calculator?
- This calculator finds the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two integers (optional third input when provided by the form).
How does GCD & LCM Calculator work?
- GCD uses the Euclidean algorithm. For two integers, LCM(a, b) = |a × b| / GCD(a, b) (with care for overflow in large products).
Why use this Math Numbers calculator?
- Use it for fraction simplification, scheduling/cycles, and number-theory homework where GCD or LCM is required.