The multiples that are shared by two or more numbers are referred to as common multiples. To explain this, let’s first define what a multiple is. A multiple of a number is the product of that number and any integer. For example, the multiples of 3 include 3, 6, 9, 12, and so on.
Now, when we look at two numbers, such as 3 and 4, we can list their multiples:
- Multiples of 3: 3, 6, 9, 12, 15, 18, …
- Multiples of 4: 4, 8, 12, 16, 20, …
From these lists, we can see that the number 12 appears in both lists. Thus, 12 is a common multiple of 3 and 4.
Common multiples can also be used to find the least common multiple (LCM), which is the smallest common multiple shared by two or more numbers. In the previous example, 12 is not just a common multiple, but it is also the least common multiple of 3 and 4.
In summary, common multiples are the multiples that two or more numbers have in common, providing a foundational concept in number theory that is essential for various mathematical applications.