What is the smallest multiple of 13?

The multiples of 13 are 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, etc. Thus, the multiples of the number 13 form a sequence where the difference between each next number and the preceding number, i.e. two consecutive multiples or products, is equal to 13. In other words, multiples of a number are the products obtained by multiplying the given number by other natural numbers. There is a difference between factors and multiples, which you can learn here. We know that 13 is a factor of 13, and also 13 is a multiple of 13.

What are the Multiples of 13?

The multiples for 13 are the numbers that are produced when 13 is multiplied by some integer, most preferably positive integers or counting numbers. That means any number that can be expressed in the form of 13n where n is an integer is a multiple of 13. So, for example, when we have two values, p and q, we say that q is a multiple of p if q = np for some integer n.

Multiples of 13 List

The list of multiples of 13 include:

13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390,…

Therefore, as per the definition mentioned above, the multiple of 13 is obtained by multiplying some integer with 13.

For example, 91, 117, 169, and 221 are all multiples of 13 for the following reasons.

We can also find the multiples through the repeated addition of a number as many times as required. We can find the first five multiples of 13 by multiplying the given number by 1, 2, 3, 4 and 5 or add the number of times as shown below:

The first multiple of 13 is: 13 × 1 = 13

The second multiple of 13 is: 13 × 2 = 26 Or 13 + 13 = 26 {here 13 is added for twice}

The third multiple of 13 is: 13 × 3 = 39 Or 13 + 13 + 13 = 39 {here 13 is added for thrice}

The fourth multiple of 13 is: 13 × 4 = 52 Or 13 + 13 + 13 + 13 = 52

The fifth multiple of 13 is: 13 × 5 = 65 Or 13 + 13 + 13 + 13 + 13 = 65

Similarly, it is possible to write several multiples of the given numbers.

Multiples of 13 Table

The first 20 multiples of 13 along with the multiplication notation in each case are tabulated below:

From the above table, we can say that the multiples of the number 13 are the results which are exactly the same as in table of 13 or the multiplication table of thirteen.

Multiples of 13 between 30 and 60

The multiples of 13 that lie between 30 and 60 are: 39 and 52.

What is a multiple and factor of 13?

We know that multiples are the n-times of any given number, whereas factors are the numbers which when multiplied together, produce the original number.

The multiples of any number could get extended till any number of times, but the factors are finite for any numbers.

The multiples of 13 are 13, 26, 39, 52, 65, etc.

The factors of 13 are 1 and 13.

Video Lesson on Common Multiples

Get the Multiples of More Numbers Here

Examples

Let’s have a look at the solved examples given below for better understanding of the concept.

Example 1:

Which two multiples of 13 are coprime numbers?

Solution:

Any of the two multiples of 13 are coprime numbers. As we know two numbers are said to be coprime if they do not have any common factors other than 1. Being multiples of 13, they always hold 13 as a common factor.

Example 2:

Write the common multiples of 13 and 17.

Solution:

The multiples of 13 are 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, etc.

The multiples of 17 are 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, etc.

Therefore, the common multiples of 13 and 17 include 221, 442, 663, and so on.

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Frequently Asked Questions on Multiples of 13