When we talk about multiples that are shared between two or more numbers, what we’re often referring to are the common multiples of those numbers. A common multiple is any number that is a multiple of each of the given numbers.
To better understand common multiples, let’s take two numbers as an example: 4 and 6.
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, …
- The multiples of 6 are: 6, 12, 18, 24, 30, …
Now, if we list out the multiples of both numbers, we can see that 12 and 24 are present in both lists. Therefore, 12 and 24 are common multiples of 4 and 6.
In general, to find common multiples of two or more numbers, you can:
- List the multiples of each number until you find a matching number.
- Alternatively, you can find the Least Common Multiple (LCM), which is the smallest common multiple of the numbers. For example, the LCM of 4 and 6 is 12.
- Once you have the LCM, you can generate other common multiples by simply adding or multiplying the LCM by whole numbers (e.g., 12, 12 imes 3 = 36, etc.).
Understanding common multiples is a fundamental concept in mathematics and is particularly useful in solving problems related to fractions, ratios, and algebra. Whether you’re working on homework or just exploring number theory, grasping this concept can enhance your mathematical skills!