LCM of two large numbers - GeeksforGeeks

19 Aug, 2020
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
Python3
// Java Program to find LCM of two large numbersimport 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 program to find LCM of two # large numbersimport math  # Function to calculate LCM of two# large numbersdef 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 Codeif __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
Output:
443593541011902763984944550799004089258248037004507648321189937329

himanshu77
GCD-LCM
large-numbers
Modular Arithmetic
Mathematical
Mathematical
Modular Arithmetic
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