Only if the numbers are co-prime.
When the two numbers are relatively prime.
Yes.
Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.
The LCM is the product of the two numbers divided by their HCF. With 12 and 13, the HCF is 1. Therefore, the LCM will equal the product. With 12 and 14, the HCF is 2. Therefore, the LCM will be half of the product.
The LCM of 4 and 6 is 12.
Their GCF will be 2. Their LCM will be half their product.
Sometimes, not always.
Their product.
If the GCF of a given pair of numbers is 1, the LCM will be equal to their product. If the GCF is greater than 1, the LCM will be less than their product. Or, stated another way, if the two numbers have no common prime factors, their LCM will be their product.
Since the product of two numbers is equal to the product of their GCF and LCM, the GCF of two numbers is equal to their product divided by their LCM and their LCM is equal to their product divided by their GCF.
The set of three numbers whose LCM (Least Common Multiple) is equal to the product of the numbers would be {1, 2, 2}. Here's how it works: LCM(1, 2, 2) = 2, which is also the product of the numbers (1 * 2 * 2 = 4).
When the two numbers are relatively prime.
The LCM of two numbers is one of the numbers when one of the numbers is a multiple of the other. The LCM of two numbers is the product of the numbers when they are relatively prime. In all other cases (like consecutive even numbers that aren't 2 and 4) the LCM is as you describe.
Yes.
800
The GCF of consecutive even numbers is 2. The LCM of consecutive even numbers is their product divided by 2.
Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.