What is the smallest common multiple of 3, as per the set of common multiples?

• A. 3
• B. 6
• C. 9
• D. 12

Answer: (A)

The smallest common multiple of a set of numbers is the smallest positive integer that is a multiple of each of the numbers in that set. In this case, the number in question is 3.

To determine the smallest common multiple of 3, consider the multiples of 3: 3, 6, 9, 12, and so forth. The first and smallest number in this list is 3 itself. Since it is a multiple of 3 (as 3 multiplied by 1 equals 3), it represents the smallest common multiple.

Understanding that a common multiple needs to be divisible by each of the numbers in the set helps clarify why 3 is the smallest common multiple specifically for the number 3. Any multiple larger than this, such as 6 or 9, is not the smallest, as they are simply larger or subsequent multiples of 3.