# 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 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 ` |

*chevron_right*

*filter_none*

**Output:**

443593541011902763984944550799004089258248037004507648321189937329

## Recommended Posts:

- Sum of two large numbers
- GCD of two numbers when one of them can be very large
- Remainder with 7 for large numbers
- Difference of two large numbers
- Divisible by 37 for large numbers
- Sort an array of large numbers
- Find Last Digit of a^b for Large Numbers
- Sum of first N natural numbers when N is extremely large
- Large Fibonacci Numbers in Java
- Writing power function for large numbers
- Multiply Large Numbers represented as Strings
- Last digit of Product of two Large or Small numbers (a * b)
- Modulo power for large numbers represented as strings
- Multiply large integers under large modulo
- Find (a^b)%m where 'b' is very large

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.