How to find Least Common Multiple (LCM) for two numbers

Question

I have used Euclid's method to find the L.C.M for two numbers.

l.c.m=a*b/(gcd(a,b))

How can I do this without using this algorithm? I have an idea of first getting all factors of these two numbers and storing them in array. Then take 1 element from array 1 and search for it in array2, if it present there then remove it from there and make the result multiply by that num.

Is this OK?

Java or C++? The solutions may be different depending on the language. — Thomas Matthews, Nov 01 '11 at 15:27
Best is to use `(a / gcd(a,b)) * b` to avoid integer overflow. Using the factorization to compute `lcm` is much less efficient than using `gcd`. — starblue, Nov 02 '11 at 07:23

score 1 · Answer 1 · answered Apr 18 '19 at 10:47

LCM(Least Common Multiple) is always greater than or equal to the larger of the two numbers. So we will first check that the larger number itself a LCM of two numbers by checking that the larger number is divisible by the smaller one , if yes we found the LCM & If no then we will increment the larger number by 1 and check again.

package com.company;
import java.util.Scanner;

public class Main {

public static void main(String args[]) {
    Scanner scan = new Scanner(System.in);
    System.out.print("Enter the first Number : ");
    int number1 = scan.nextInt();
    System.out.print("Enter the second number : ");
    int number2 =scan.nextInt();

    int multiple;

    if(number1 >= number2) {
        multiple = number1;
    } else {
        multiple = number2;
    }

    Boolean loopContinue = true;

    while(loopContinue) {
        if(multiple % number1 == 0 && multiple % number2 == 0) {
            System.out.println("LCM of Two Numbers is " + multiple);
            loopContinue = false;
        }
        multiple++;
    }
  }
}

Thiruvengaden_R · Answer 2 · 2023-06-29T13:58:48.760

**LCM of two numbers using while loop**

package whileloop1;

import java.util.Scanner;

public class Lcm {

public static void main(String[] args) {
    Lcm obj = new Lcm();
    obj.twoNumberLcm();
}
void twoNumberLcm       
{
    Scanner Sobj = new Scanner(System.in);
    System.out.println("Enter your First Number ");
    int num1 = Sobj.nextInt();
    System.out.println("Enter your Second Number ");
    int num2 = Sobj.nextInt();
    int big,small;
    if(num1>num2)
    {
        big = num1;
        small = num2;
    }
    else
    {
        big = num2;
        small = num1;
    }
    System.out.println(" Bigger number is " + big);
    System.out.println(" Smaller number is " + small);
    int smallcopy = small;
    int bigcopy = big;
    int count =1;
    while(count>0)
    {
        while(big>=small)
        {
            if(big == small)
            {
                System.out.println("Least common mutiples of given two numbers" + small);
                count--;
                break;
            }
            small=small+smallcopy;
        }
        big = big+bigcopy;
    }
}

score 1 · Answer 3 · answered Nov 01 '11 at 15:03

1

I believe the algorithm you suggest is a method using a table, check to see if it works for you.

answered Nov 01 '11 at 15:03

Óscar López

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His method is actually [Prime Factorization](https://secure.wikimedia.org/wikipedia/en/wiki/Least_common_multiple#Finding_least_common_multiples_by_prime_factorization). But yeah, it works. – MSalters Nov 01 '11 at 15:16

MSalters · Accepted Answer · 2011-11-03T10:21:28.993

1

Almost. What's the LCM of 4 and 8? Obviously 8 (2³), but in your method you'd find 2. You need to keep track not just of all factors, but also how often they appear.

edited Nov 03 '11 at 10:21

answered Nov 01 '11 at 15:18

MSalters

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Isn't the LCM of 4 and 8 actually 8, not 4? And GCD(8,4) yields 4, so (8*4)/4 = 8, so the formula in the question generates the correct answer? The LCM has to be at least as big as the larger of the two input values (assuming all positive numbers). – Jonathan Leffler Nov 01 '11 at 18:24
Eh, yes, fixed. The GCD and LCM methods are quite closely related. If you factor both terms in prime factors, take the respective minimums, and multiply them, you get the GCD (here: min(2,3)=2, 2x2=4). Take the respctive maximums (here: max(2,3)=3, 2x2x2=8) and you get the LCM. – MSalters Nov 03 '11 at 10:24

score 0 · Answer 5 · answered Dec 28 '18 at 08:03

You can get LCM of two number by getting GCD at first. Here is the solution for the above.

package com.practice.competitive.maths;

import java.util.Scanner;

public class LCMandGCD {

    public static void main(String[] args) {
        try (Scanner scanner = new Scanner(System.in)) {
            int testCases = scanner.nextInt();
            while (testCases-- > 0) {
                long number1 = scanner.nextInt();
                long number2 = scanner.nextInt();
                long gcd = computeGCD(number1, number2);
                long lcm = computeLCM(number1, number2, gcd);
                System.out.println(lcm + " " + gcd);
            }
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private static long computeGCD(long number1, long number2) {
        while (number1 != number2) {
            if (number1 > number2)
                number1 -= number2;
            else
                number2 -= number1;
        }   
        return number2;
    }

    private static long computeLCM(long number1, long number2, long gcd) {
        return (number1*number2)/gcd;
    }

}

How to find Least Common Multiple (LCM) for two numbers

5 Answers5