Given three integers x, y, z, the task is to compute the value of **GCD(LCM(x,y), LCM(x,z))**.

Where, GCD = Greatest Common Divisor, LCM = Least Common Multiple

Examples:

Input: x = 15, y = 20, z = 100 Output: 60 Input: x = 30, y = 40, z = 400 Output: 120

One way to solve it is by finding GCD(x, y), and using it we find LCM(x, y). Similarly, we find LCM(x, z) and then we finally find the GCD of the obtained results.

An efficient approach can be done by the fact that the following version of distributivity holds true:

GCD(LCM (x, y), LCM (x, z)) = LCM(x, GCD(y, z))

For example, GCD(LCM(3, 4), LCM(3, 10)) = LCM(3, GCD(4, 10)) = LCM(3, 20) = 60

This reduces our work to compute the given problem statement.

// C++ program to compute value of GCD(LCM(x,y), LCM(x,z)) #include<bits/stdc++.h> using namespace std; // Returns value of GCD(LCM(x,y), LCM(x,z)) int findValue(int x, int y, int z) { int g = __gcd(y, z); // Return LCM(x, GCD(y, z)) return (x*g)/__gcd(x, g); } int main() { int x = 30, y = 40, z = 400; cout << findValue(x, y, z); return 0; }

Output:

120

As a side note, vice versa is also true, i.e., gcd(x, lcm(y, z)) = lcm(gcd(x, y), gcd(x, z)

**Reference:**

https://en.wikipedia.org/wiki/Distributive_property#Other_examples

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