## C++, math, least_common_multiple.cpp

``````/**
* @file
*
* A basic implementation of LCM function
*/

#include <cassert>
#include <iostream>

/**
* Function for finding greatest common divisor of two numbers.
* @params two integers x and y whose gcd we want to find.
* @return greatest common divisor of x and y.
*/
unsigned int gcd(unsigned int x, unsigned int y) {
if (x == 0) {
return y;
}
if (y == 0) {
return x;
}
if (x == y) {
return x;
}
if (x > y) {
// The following is valid because we have checked whether y == 0

unsigned int temp = x / y;
return gcd(y, x - temp * y);
}
// Again the following is valid because we have checked whether x == 0

unsigned int temp = y / x;
return gcd(x, y - temp * x);
}

/**
* Function for finding the least common multiple of two numbers.
* @params integer x and y whose lcm we want to find.
* @return lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y)
*/
unsigned int lcm(unsigned int x, unsigned int y) {
return x / gcd(x, y) * y;
}

/**
* Function for testing the lcm() functions with some assert statements.
*/
void tests() {
// First test on lcm(5,10) == 10
assert(((void)"LCM of 5 and 10 is 10 but lcm function gives a different "
"result.\n",
lcm(5, 10) == 10));
std::cout << "First assertion passes: LCM of 5 and 10 is " << lcm(5, 10)
<< std::endl;

// Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)
assert(((void)"LCM of 2 and 3 is 6 but lcm function gives a different "
"result.\n",
lcm(2, 3) == 6));
std::cout << "Second assertion passes: LCM of 2 and 3 is " << lcm(2, 3)
<< std::endl;

// Testing an integer overflow.
// The algorithm should work as long as the result fits into integer.
assert(((void)"LCM of 987654321 and 987654321 is 987654321 but lcm function"
" gives a different result.\n",
lcm(987654321, 987654321) == 987654321));
std::cout << "Third assertion passes: LCM of 987654321 and 987654321 is "
<< lcm(987654321, 987654321)
<< std::endl;
}

/**
* Main function
*/
int main() {
tests();
return 0;
}
``````