Choose all the numbers that are common multiples of 6 and 9 . \( \square 3 \quad \square \quad \square 9 \square 15 \quad \square \)

To be a common multiple of 6 and 9, a number must be divisible by both 6 and 9. In other words, it must be a multiple of the least common multiple (LCM) of 6 and 9. The first step is to find that LCM. Step 1. Find the prime factorizations:  • 6 = 2 × 3  • 9 = 3 × 3 = 3² Step 2. Determine the LCM by taking the highest power of each prime:  • For 2: the highest power is 2¹ (from 6).  • For 3: the highest power is 3² (from 9). Thus, LCM(6, 9) = 2 × 3² = 2 × 9 = 18. Step 3. Any common multiple of 6 and 9 must be a multiple of 18. The first few common multiples are 18, 36, 54, and so on. Now, looking at the numbers given:  • 3, 9, and 15 are the numbers listed.  • 3 ÷ 6 is not an integer, and 3 ÷ 9 is not an integer.  • 9 ÷ 6 is not an integer, even though 9 ÷ 9 = 1.  • 15 ÷ 6 and 15 ÷ 9 are also not integers. Since none of these numbers is divisible by both 6 and 9, none of them is a common multiple of 6 and 9. Therefore, none of the provided numbers (3, 9, 15) are common multiples. The correct common multiples start at 18 (then 36, 54, etc.).