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The LCM can be calculated without using any loop or condition as follows:

int lcm (int a, int b) {
return a / gcd (a, b) * b;
}

The problem is that the typical implementation for the GCD function uses Euclid's algorithm, which requires a conditional loop:
int gcd (int a, int b) {
while (b!=0) b ^= a ^= b ^= a %= b;
return a;
}


So the question is really how do we calculate the GCD without a conditional loop, not the LCM. The answer is that we cannot. There are certainly alternatives to Euclid's algorithm, but they all involve conditional loops. Although recursion isn't technically a loop, it still requires a conditional expression to terminate the recursion.
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