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

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

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

How to solve it without using GCD?
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### Re: Prove that LCM(x, y) is primitive recursive.

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.

If you're stuck on any particular step or need further clarification, feel free to ask! Just contact us by visiting mathsassignmenthelp.com or call us on +1 (315) 557-6473.
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