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