LCM of two large numbers

Given two large numbers ‘a’ and ‘b’ such that(10^20<=a, b<=10^300). Find the LCM of two large numbers given. Examples:

 Input: a = 234516789234023485693020129
        b = 176892058718950472893785940
 Output: 41484157651764614525905399263631111992263435437186260

 Input: a = 36594652830916364940473625749407
        b = 448507083624364748494746353648484939
 Output: 443593541011902763984944550799004089258248037004507648321189937329

Solution: In the given problem, we can see that the number are very large which is outside the limit of all available primitive data types, so we have to use the concept of BigInteger Class in Java. So we convert the given strings into biginteger and then we use java.math.BigInteger.gcd(BigInteger val) method to compute gcd of large numbers and then we calculate lcm using following formula: LCM * HCF = x * y, where x and y are two numbers Below is implementation of the above idea. 

Java

// Java Program to find LCM of two large numbers
import java.math.*;
import java.lang.*;
import java.util.*;

public class GFG {

    // function to calculate LCM of two large numbers
    public static BigInteger lcm(String a, String b)
    {
        // convert string 'a' and 'b' into BigInteger
        BigInteger s = new BigInteger(a);
        BigInteger s1 = new BigInteger(b);

        // calculate multiplication of two bigintegers
        BigInteger mul = s.multiply(s1);

        // calculate gcd of two bigintegers
        BigInteger gcd = s.gcd(s1);

        // calculate lcm using formula: lcm * gcd = x * y
        BigInteger lcm = mul.divide(gcd);
        return lcm;
    }

    // Driver Code
    public static void main(String[] args)
    {

        // Input 'a' and 'b' are in the form of strings because
        // they can not be handled by integer data type
        String a = "36594652830916364940473625749407";
        String b = "448507083624364748494746353648484939";

        System.out.print(lcm(a, b));
    }
}
// Code contributed by Saurav Jain

Python3

# Python3 program to find LCM of two
# large numbers
import math

# Function to calculate LCM of two
# large numbers
def lcm (a, b):

    # Convert string 'a' and 'b'
    # into Integer
    s = int(a)
    s1 = int(b)

    # Calculate multiplication of
    # both integers
    mul = s * s1

    # Calculate gcd of two integers
    gcd = math.gcd(s, s1)

    # Calculate lcm using
    # formula: lcm * gcd = x * y
    lcm = mul // gcd

    return lcm

# Driver Code
if __name__ == '__main__':

    # Input 'a' and 'b' are in the
    # form of strings
    a = "36594652830916364940473625749407"
    b = "448507083624364748494746353648484939"

    print(lcm(a, b))

# This code is contributed by himanshu77

Javascript

// JavaScript program to find LCM of two
// large numbers
function __gcd(a, b)
{
    if (b == 0n)
        return a;
    return __gcd(b, a % b);
}

// Function to calculate LCM of two
// large numbers
function lcm (a, b)
{

    // Convert string 'a' and 'b'
    // into Integer
    let s = BigInt(a);
    let s1 = BigInt(b);

    // Calculate multiplication of
    // both integers
    let mul = s * s1;

    // Calculate gcd of two integers
    let gcd = __gcd(s, s1);

    // Calculate lcm using
    // formula: lcm * gcd = x * y
    let lcm = (mul - (mul % gcd)) / gcd;

    return lcm;
}

// Driver Code

//  Input 'a' and 'b' are in the
// form of strings
let a = "36594652830916364940473625749407";
let b = "448507083624364748494746353648484939";

console.log(lcm(a, b));

//  This code is contributed by phasing17

Output:

443593541011902763984944550799004089258248037004507648321189937329