by Guest » Mon Jun 10, 2024 8:01 am
To prove that the function lcm(x,y) is primitive recursive without using the greatest common divisor (GCD), you can use the following steps:
Define lcm(x, y): The least common multiple (LCM) of two numbers x and y is the smallest positive integer that is divisible by both x and y.
Enumerate Multiples:
Start enumerating multiples of x and y until you find a common multiple. The first common multiple you encounter will be the least common multiple.
Check for Divisibility:
For each multiple of x and y, check if it is divisible by both x and y. Once you find such a number, it is the least common multiple.
Algorithm:
Construct a primitive recursive algorithm based on the above steps to find the LCM of x and y.
By following these steps, you can demonstrate that the function lcm(x,y) is primitive recursive without relying on the GCD.
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