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Posted 24 Feb 2011


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Fast Integer Algorithms: Greatest Common Divisor and Least Common Multiple, .NET solution

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4.71/5 (10 votes)
19 Apr 2011CPOL1 min read
.NET/C# managed code implementation of 2 core algorithms of integer arithmetic: GCD and LCM (used in "3 Fraction Calculator", best on Google)

Fast GCD and LCM algorithms

The following code snippets demonstrate the programmatic solution to the fundamental integer-math problems of finding:

  • Greatest Common Divisor, or GCD
  • Least Common Multiple, or LCM

The solution is implemented as managed .NET code written in C# 4, applicable to the previous versions as well. It is portable to other languages, most notably, to the VB family (VB/VBA/VB.NET), Java and JavaScript as well, provided that the syntax differences are properly addressed.

GCD and LCM calculations are essential for fractions arithmetic: corresponding algorithms are implemented in the free online "3 Fractions Calculator" (topping Google/Yahoo search list), available at:[^].

Mobile version of the Fractions Calculator optimized for smart phones is available at [4]: you could see the image of Mobile Fraction Calculator running in iPad 2 (the picture has been taken at iPad 2 weekend in NY Apple store).

Another core Prime Factoring and corresponding Primality test algorithm has been described in the previous post on CodeProject [3]: corresponding demo is available at [2].
// Author           :   Alexander Bell
// Copyright        :   2007-2011 Infosoft International Inc
// Date Created     :   01/15/2007
// Last Modified    :   01/11/2011
// Description      :   Find Greatest Common Divisor (GCD) and
//                  :   Least Common Multiple (LCM) 
//                  :   of two Int64 using Euclid algorithm
// DISCLAIMER: This Application is provide on AS IS basis without any warranty

// TERMS OF USE     :   This module is copyrighted.
//                  :   You can use it at your sole risk provided that you keep
//                  :   the original copyright note.
using System;

namespace Infosoft.Fractions
    public static partial class Integers
        #region GCD of two integers
        /// <summary>
        /// find Greatest Common Divisor (GCD) of 2 integers
        /// using Euclid algorithm; ignore sign
        /// </summary>
        /// <param name="Value1">Int64</param>
        /// <param name="Value2">Int64</param>
        /// <returns>Int64: GCD, positive</returns>
        public static Int64 GCD( Int64 Value1, Int64 Value2)
            Int64 a;            // local var1
            Int64 b;            // local var2
            Int64 _gcd = 1;     // Greates Common Divisor

                // throw exception if any value=0
                if(Value1==0 || Value2==0)   {
                    throw new ArgumentOutOfRangeException(); 

                // assign absolute values to local vars
                a = Math.Abs(Value1);
                b = Math.Abs(Value2); 

                // if numbers are equal return the first
                if (a==b) {return a;}
               // if var "b" is GCD return "b"
                else if (a>b && a % b==0) {return b;}
               // if var "a" is GCD return "a"
                else if (b>a && b % a==0) {return a;}

                // Euclid algorithm to find GCD (a,b):
                // estimated maximum iterations: 
                // 5* (number of dec digits in smallest number)
                while (b != 0) {
                    _gcd = b;
                    b = a % b;
                    a = _gcd;
                return _gcd;
            catch { throw; }

        #region LCM of two integers
        /// <summary>
        /// Find Least common Multiply of 2 integers
        /// using math formula: LCM(a,b)= a*(b/GCD(a,b));
        /// </summary>
        /// <param name="Value1">Int64</param>
        /// <param name="Value2">Int64</param>
        /// <returns>Int64</returns>
        public static Int64 LCM(Int64 Value1, Int64 Value2)
                Int64 a = Math.Abs(Value1);
                Int64 b = Math.Abs(Value2);

                // perform division first to avoid potential overflow
                a = checked((Int64)(a / GCD(a, b)));
                return checked ((Int64)(a * b));
            catch { throw; }

Notice that checked keyword ensures that the algorithm properly raises the exception in case of overflow, so preventing the potentially erroneous results being unchecked and returned by function.

Mobile Fraction Calculator on iPad 2


1. 3 Fraction Calculator (best on Google)[^]
2. Prime Factoring Calculator[^]
3. Fast Prime Factoring Algorithm[^]
4. Fraction Calculator, Mobile version[^]


This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)


About the Author

Software Developer (Senior)
United States United States
Dr. Alexander Bell is a seasoned full-stack Software Engineer (Win/Web/Mobile). He holds PhD in Electrical and Computer Engineering, authored 37 inventions and published 300+ technical articles. Currently focused on multiple Android/Mobile development projects and Big Data' Machine Learning, AI, IoT. Alex participated in App Innovation Contests (AIC 2102/2013) with multiple winning submissions. Sample portfolio apps and publications:

  1. Aggregate Product function extends SQL
  2. Use SQL to generate large data sequence
  3. HTML5/CSS3 graphic enhancement: buttons, inputs
  4. Advanced CSS3 Styling of HTML5 SELECT Element
  5. YouTube™ API for ASP.NET
  6. HTML5 Tables Formatting: Alternate Rows, Color Gradients, Shadows

Comments and Discussions

GeneralMy vote of 2 Pin
carga16-Dec-13 4:09
Membercarga16-Dec-13 4:09 
Questionany of two = 0... Pin
Andrei Zakharevich1-Nov-13 6:40
MemberAndrei Zakharevich1-Nov-13 6:40 
GeneralMy vote of 5 Pin
JBoada7-Aug-13 8:59
MemberJBoada7-Aug-13 8:59 
GeneralRe: My vote of 5 Pin
DrABELL7-Aug-13 10:09
MemberDrABELL7-Aug-13 10:09 
GeneralThanks, Hayk! Best rgds, Alex Pin
DrABELL3-Mar-11 3:35
MemberDrABELL3-Mar-11 3:35 
GeneralReason for my vote of 2 This is the known algorithm of Eucli... Pin
Hayk Aleksanyan28-Feb-11 18:25
MemberHayk Aleksanyan28-Feb-11 18:25 
GeneralRe: Hayk, The solution clearly states that it is using a Euclid ... Pin
DrABELL1-Mar-11 2:05
MemberDrABELL1-Mar-11 2:05 
GeneralRe: Hayk, I would appreciate if you could re-consider your vote ... Pin
DrABELL2-Mar-11 3:45
MemberDrABELL2-Mar-11 3:45 
Generalmay want to fix your formatting though :) Pin
jfriedman25-Feb-11 8:41
Memberjfriedman25-Feb-11 8:41 
GeneralReason for my vote of 3 Cleaner than last time... Pin
jfriedman25-Feb-11 2:32
Memberjfriedman25-Feb-11 2:32 
GeneralRe: You should seriously re-consider your voting practice Pin
DrABELL8-Mar-11 1:06
MemberDrABELL8-Mar-11 1:06 

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