Question

How can you tell when the LCM of two numbers will equal one of the numbers or equal the product of the numbers

Answer 1

When one number will divide exactly into the other one then the other one will be the LCM. For example the LCM of 4 and 8 = 8 .

When they do not divide as above then the product of the numbers may be the LCM. For example the LCM of 3 and 4 = 3*4  = 12.  

The product is not always the LCM.  It might be a lower number . For example the LCM of 4  and 6 is not  24  but 12.  ( 24 / 2).