2. Here are the first three multiples of 8 : \[ 8,16,24, \ldots \] Here are the first three multiples of 12 : \[ 12,24,36, \ldots \] What are the next three numbers that are on both lists? Explain or show your reasoning. When

The next three numbers that are on both lists can be found by identifying the least common multiples (LCM) of 8 and 12. The LCM of 8 and 12 is 24, which is the first number in both lists. The subsequent multiples can be found by continuing to add the LCM: \( 2 \times 24 = 48 \) and \( 3 \times 24 = 72 \). Thus, the next three numbers are 24, 48, and 72. You can also think of it as finding numbers that both 8 and 12 divide evenly into. Since both lists are based on multiples, just keep counting up in increments of both 8 and 12 until they sync up again! For example, the fourth and fifth multiples of 12 would lead you to 48 and 72, confirming that these are indeed shared members of both multiple families.