Greatest Common Divisor (GCD) & Least Common Multiple (LCM) Calculator

Run the Euclidean algorithm on two or three integers to find GCD and LCM.

Greatest Common Divisor GCD(a, b, c)
12
Least Common Multiple LCM(a, b, c) 720
Pairwise GCD(a, b) 12
Pairwise LCM(a, b) 720
Inputs
First positive integer a.
Second positive integer b.
Third positive integer c.
Results & Graph
Greatest Common Divisor GCD(a, b, c)
12
Least Common Multiple LCM(a, b, c)
720
Pairwise GCD(a, b)
12
Pairwise LCM(a, b)
720

Greatest Common Divisor GCD(a, b, c)

Graph 1 • Int A Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 32.4 64.8 50%: 12 12 50% 75%: 12 12 75% 100%: 12 12 100% 125%: 60 60 125% 150%: 12 12 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Greatest Common Divisor GCD(a, b, c) 12 Least Common Multiple LCM(a, b, c) 720 Pairwise GCD(a, b) 12 Pairwise LCM(a, b) 720
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Greatest Common Divisor GCD(a, b, c)12Least Common Multiple LCM(a, b, c)720Pairwise GCD(a, b)12Pairwise LCM(a, b)720
Summary: For (48, 180, 120), GCD = 12 and Least Common Multiple LCM = 720.
Summary: For (48, 180, 120), GCD = 12 and Least Common Multiple LCM = 720.

Formula & Mathematical Methodology: GCD & LCM Mathematical Identity

LCM(a, b) = |a × b| / GCD(a, b)
LCM(a, b) = |a × b| / GCD(a, b)
  • intA: Int A (numeric parameter)
  • intB: Int B (numeric parameter)
  • intC: Int C (numeric parameter)

Rounding: All calculations run in double-precision IEEE-754 arithmetic; displayed outputs round to up to 4 decimal places.

Worked Example: Worked Mathematical Verification: GCD & LCM

Run the Euclidean algorithm on two or three integers to find GCD and LCM.

  1. Verify the domain constraints of the input parameters.
  2. Apply the governing mathematical identity: LCM(a, b) = |a × b| / GCD(a, b).
  3. Cross-check the primary value against the supporting invariants and coordinate graph.
Result: Evaluates GCD & LCM via LCM(a, b) = |a × b| / GCD(a, b).

Frequently Asked Questions

What mathematical formula does the Greatest Common Divisor (GCD) & Least Common Multiple (LCM) Calculator use?

It directly evaluates LCM(a, b) = |a × b| / GCD(a, b) in double-precision floating-point arithmetic and updates all supporting invariants and graphs live.

How can I compare different parameter sets?

Click Compare in the results toolbar to pin up to three parameter combinations side by side.

Can I export the mathematical report or share a link?

Yes. Use the Share Link, Copy Summary, or Markdown/JSON export buttons in the results panel.

Mathematics & Statistics • Number Theory Guide

How to Use the Greatest Common Divisor (GCD) & Least Common Multiple (LCM) Calculator: Practical Guide & Visual Analysis

Calculate Greatest Common Divisor (GCD), Least Common Multiple (LCM), and Bézout identity check for integers. Includes textbook mathematical notation, step-by-step verification, and three custom SVG visualizations. Whether you are researching greatest common divisor (gcd) & least common multiple (lcm) calculator, gcd & lcm, gcd lcm euclidean algorithm, number theory calculator, this interactive tool helps you calculate Greatest Common Divisor (GCD), Least Common Multiple (LCM), and Bézout identity check for integers.

Interpreting the 3 Custom Visual Graphs & Key Outputs

As you adjust Int A, Int B, Int C, the calculator immediately computes Primary exact or numerical solution, Supporting identities & invariants, 3-Panel mathematical SVG plots and updates all three domain-specific SVG charts in real time. Instead of relying on a single static figure, you can inspect the primary domain diagram, component breakdown, and multi-point trajectory curve to see how changing your inputs shifts the final result. Use the Compare (up to 3 scenarios) button to evaluate side-by-side variations before making a decision.

Real-World Benchmark & Planning Tips (Universal Mathematical & Statistical Standard (ISO 80000-2))

In our benchmark scenario (Worked Mathematical Verification: GCD & LCM), Evaluates GCD & LCM via LCM(a, b) = |a × b| / GCD(a, b). Keep in mind that uses standard Euclidean geometry, real/complex algebra, and NIST statistical definitions. For related calculations in Mathematics & Statistics, explore Scientific Calculator, Statistics & Standard Deviation Calculator, Geometry Calculator (Right Triangle, Circle & Cylinder).