# LCM of two large numbers

• Difficulty Level : Medium
• Last Updated : 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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`

Output:

```443593541011902763984944550799004089258248037004507648321189937329
```

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