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What are the Multiples of 14?
The multiples of 14 are the numbers that can be obtained by multiplying 14 by an integer. In other words, if you take 14 and multiply it by 1, 2, 3, and so on, you will get the multiples of 14. Let’s explore the multiples of 14 up to a certain point.
Starting with 14 itself, the first few multiples are 14, 28, 42, 56, 70, 84, and 98. These numbers are obtained by multiplying 14 by 1, 2, 3, 4, 5, 6, and 7, respectively.
Continuing this pattern, the next set of multiples includes 112, 126, 140, 154, 168, 182, and 196. These numbers are generated by multiplying 14 by 8, 9, 10, 11, 12, 13, and 14, respectively.
The multiples of 14 continue indefinitely. As you move further along the number line, you encounter 210, 224, 238, 252, 266, 280, and 294. Each of these results from multiplying 14 by the corresponding integers 15, 16, 17, 18, 19, 20, and 21.
It’s important to note that the multiples of 14 are infinite, as you can always find a larger multiple by multiplying 14 by a larger integer. In summary, the multiples of 14 form a sequence of numbers that are evenly divisible by 14, and this sequence extends infinitely in both directions along the number line.
What are Multiples?
In mathematics, a multiple is the product of a number and an integer. In other words, if you multiply a number by an integer, the result is a multiple of that number. For example, 4 is a multiple of 2 because 4 = 2 × 2.
Every integer is a multiple of 1. Zero is a multiple of every integer.
We can also use the concept of multiples to define common multiples and least common multiples.
A common multiple of two or more numbers is a number that is a multiple of each of those numbers. For example, 12 is a common multiple of 3 and 4 because 12 = 3 × 4.
The least common multiple of two or more numbers is the smallest number that is a common multiple of those numbers. For example, 12 is the least common multiple of 3 and 4.
Multiples are an important concept in mathematics and have many applications, such as in arithmetic, algebra, and geometry.
How to Find the Multiples of 14?
A multiple of a number is the product of that number and any integer. To find the multiples of 14, you can simply multiply 14 by any integer. Here are the first few multiples of 14:
14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350, …
As you can see, the pattern is simple: each multiple of 14 is 14 more than the previous multiple. This is because 14 is being multiplied by an integer, and each integer is one more than the previous integer.
Here are some other ways to find the multiples of 14:
- Use a calculator: Simply type in 14 and then press the multiplication key repeatedly, adding 1 to the second number each time.
- Use a multiplication table: A multiplication table shows the products of two numbers. You can find a multiplication table of 14 by searching online or in a math textbook.
- Use a pattern: As mentioned above, the multiples of 14 follow a simple pattern: each multiple is 14 more than the previous multiple. You can use this pattern to find any multiple of 14, even if you don’t have a calculator or multiplication table handy.
Multiples of 14 Table
| Number | Multiple of 14 |
|---|---|
| 1 | 14 |
| 2 | 28 |
| 3 | 42 |
| 4 | 56 |
| 5 | 70 |
| 6 | 84 |
| 7 | 98 |
Properties of Common Multiples
Common multiples are multiples that are shared by two or more numbers. In other words, if a number is a multiple of two or more numbers, then it is a common multiple of those numbers. For example, the numbers 12, 24, and 36 are all common multiples of the numbers 2, 3, and 4.
Here are some properties of common multiples:
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Every multiple of a number is a common multiple of that number and itself. For example, every multiple of 4 is a common multiple of 4 and 4, such as 4, 8, 12, and so on.
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The product of two numbers is always a common multiple of those two numbers. For example, the product of 6 and 8 is 48, which is a common multiple of 6 and 8.
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The least common multiple (LCM) of two numbers is the smallest positive integer that is a common multiple of those two numbers. For example, the LCM of 6 and 8 is 24.
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Two numbers have an infinite number of common multiples. This is because the multiples of any number continue indefinitely.
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The common multiples of two or more numbers can be found by listing the multiples of the larger number until a multiple is found that is divisible by the smaller number. For example, the common multiples of 6 and 8 are 24, 48, 72, and so on.
These properties can be used to solve a variety of math problems, such as finding the LCM of two numbers or determining whether two numbers have any common multiples.
Solved Examples of Multiples of 14
Here are some solved examples of multiples of 14:
Example 1:
Find the first 10 multiples of 14.
Solution:
The first 10 multiples of 14 are:
14, 28, 42, 56, 70, 84, 98, 112, 126, 140
Example 2:
Determine whether 126 is a multiple of 14.
Solution:
Yes, 126 is a multiple of 14 because 126 ÷ 14 = 9.
Example 3:
List the next 5 multiples of 14 after 140.
Solution:
The next 5 multiples of 14 after 140 are:
154, 168, 182, 196, 210
