I was trying to coerce gpt-4o to talk about the gcd and lcm in terms of sets of the prime factors where the product is the union of the sets, gcd is the interse

I was trying to coerce gpt-4o to talk about the gcd and lcm in terms of sets of the prime factors where the product is the union of the sets, gcd is the intersection, and the lcm is the union less the intersection and it kept telling me I was incorrect and being "non standard". It has a long, long way to go.