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

[SimonaB]

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

How to solve it without using GCD?

 

[Dr.Peterson]

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

How to solve it without using GCD?

Are you asking how to write a program to find the least common multiple? (Note: it's "multiple", not "multiplier".)

There are many ways to do it, How would you find the LCM of, say, 6 and 8, if you'd never heard of the GCD concept? (There was probably a time when you did exactly that.) You aren't looking for a particularly efficient algorithm, just what a child might do when they learn about LCM.

If that's not what you want to do, you will need to state the definition you have been given for "primitive recursive function", and any theorems that are available for you to use in a proof.