Final answer:
To determine when the LCM of two numbers is equal to one of the numbers or the product of the numbers, you need to understand the concept of factors. The LCM is the smallest multiple that two numbers have in common. If one of the numbers is a factor of the other number, then the LCM will be that number. If the two numbers share no common factors, then the LCM will be the product of the numbers.
Step-by-step explanation:
How to Tell When the LCM (Least Common Multiple) of Two Numbers is Equal to One of the Numbers or the Product of the Numbers
To determine when the LCM of two numbers is equal to one of the numbers or the product of the numbers, you need to understand the concept of factors. The LCM is the smallest multiple that two numbers have in common. If one of the numbers is a factor of the other number, then the LCM will be that number. If the two numbers share no common factors, then the LCM will be the product of the numbers.
For example, let's find the LCM of 4 and 6. The factors of 4 are 1, 2, and 4, while the factors of 6 are 1, 2, 3, and 6. The smallest multiple they share in common is 2, so the LCM of 4 and 6 is 2.
On the other hand, if we want to find the LCM of 3 and 8, the factors of 3 are 1 and 3, while the factors of 8 are 1, 2, 4, and 8. There are no common factors between them, so the LCM is the product of 3 and 8, which is 24.