Fast Greatest Common Divisor and Least Common Multiple Algorithms

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. Another Prime Factoring and corresponding Primality test algorithm has been described in the previous post on CodeProject [1].

//============================================================================
// 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

            try
            {
                // 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; }
        }
        #endregion

        #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)
        {
            try
            {
                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; }
        }
        #endregion
    }
}
//***************************************************************************

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.

References

1. Fast Prime Factoring Algorithm[^]