In a example 4 grant finds applesauce that comes in packages of 8 but now he finds juice bottles in only packages of 3 will the LCM change?

The least common multiple (LCM) of two numbers changes when the quantities of those numbers change. In this case, the LCM of 8 (Applesauce packages) and 3 (juice bottle packages) is 24, which remains the same regardless of how many packages you have. Thus, while the LCM itself does not change, the total number of items you would need to purchase to achieve an equal number of both products will be determined by those quantities.