๐ What are Multiples?
A multiple of a number is simply that number multiplied by any whole number (1, 2, 3, and so on). Think of it as the result you get when you skip count by that number!
- ๐ข For example, the multiples of 3 are: 3, 6, 9, 12, 15, and so on... (3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, etc.)
- ๐ก The multiples of 7 are: 7, 14, 21, 28, 35, and so on...
- ๐ In mathematical terms, if $a$ and $b$ are integers, and $b = na$ for some integer $n$, then $b$ is a multiple of $a$.
๐ค What are Common Multiples?
Common multiples are multiples that are shared between two or more numbers. To find them, list out the multiples of each number and see which ones they have in common.
- ๐ For example, let's find the common multiples of 2 and 3:
- โ Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...
- โ Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...
- โ
Common multiples of 2 and 3: 6, 12, 18, 24...
๐ Common Multiples vs. Multiples: A Comparison
| Feature |
Multiples |
Common Multiples |
| Definition |
The result of multiplying a number by an integer. |
Multiples shared by two or more numbers. |
| Number of Numbers Involved |
Applies to a single number. |
Requires at least two numbers. |
| Example |
Multiples of 5: 5, 10, 15, 20... |
Common multiples of 4 and 6: 12, 24, 36... |
| Finding Them |
Multiply the number by integers. |
List multiples of each number and find the shared ones. |
๐ Key Takeaways
- โจ Multiples are what you get when you multiply a number by any whole number.
- ๐ Common multiples are multiples that two or more numbers share.
- ๐งฎ To find common multiples, list the multiples of each number and identify the ones they have in common.