diff --git a/math/least_common_multiple.cpp b/math/least_common_multiple.cpp new file mode 100644 index 000000000..741945716 --- /dev/null +++ b/math/least_common_multiple.cpp @@ -0,0 +1,70 @@ +/** + * Copyright 2020 @author tjgurwara99 + * @file + * + * A basic implementation of LCM function + */ + +#include +#include + +/** + * 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 + + int temp = x / y; + return gcd(y, x - temp * y); + } + // Again the following is valid because we have checked whether x == 0 + + 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 * y / gcd(x, 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; +} + +/** + * Main function + */ +int main() { + tests(); + return 0; +}