Question

The LCM of two numbers that have no common factors is their product.


True

False

Answer 1

False. Either of the two numbers cannot be divisible by their product.
1 is a common factor but is normally not considered an answer.

Answer 2

I think you misunderstood the question. We are talking about the least common multiple here, not the greatest common factor, so we don't need that the LCM divides the two numbers. It should be the other way around.

As for the question itself, try using the fact that if two numbers \(a\text{ and } b\) have no common factors (other than 1), then \(\gcd(a,b)=1\), and: $$\text{lcm}(a,b)\cdot\gcd(a,b)=ab.$$