Prove that LCM(x, y) is primitive recursive.

[Guest]

Prove that function lcm(x, y) =“the least common multiplier of x and y” is primitive recursive.

How to solve it without using GCD?

[Guest]

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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