Thirteen is a number with a lot of interesting properties, including the fact that it is a prime number. In mathematics, a multiple of a number is simply another number that can be divided evenly into the original number. In this article, we will take a closer look at the multiples of 13, and explore some of the interesting patterns and properties that emerge when working with this number.
Contents
What are Multiples?
Before we dive into the multiples of 13, let’s first define what multiples are. A multiple is a number that can be divided evenly by another number. For example, 12 is a multiple of 4 because 12 can be divided evenly by 4 (12 ÷ 4 = 3). In mathematical terms, we write this as 12 = 4 x 3.
The Multiples of 13
The first multiple of 13 is 13 itself. From there, the pattern continues with 26, 39, 52, and so on. These are all the numbers that can be divided evenly by 13.
One interesting pattern to note is that the sum of the digits of the multiples of 13 is always a multiple of 13. For example, the sum of the digits in the number 26 is 2 + 6 = 8, which is not a multiple of 13. But the sum of the digits in the number 39 is 3 + 9 = 12, which is a multiple of 13.
Multiples of 13 Table
The first 20 multiples of 13 along with the multiplication notation in each case are tabulated below:
| Multiplication of 13 with numbers | Multiples of 13 |
| 13 × 1 | 13 |
| 13 × 2 | 26 |
| 13 × 3 | 39 |
| 13 × 4 | 52 |
| 13 × 5 | 65 |
| 13 × 6 | 78 |
| 13 × 7 | 91 |
| 13 × 8 | 104 |
| 13 × 9 | 117 |
| 13 × 10 | 130 |
| 13 × 11 | 143 |
| 13 × 12 | 156 |
| 13 × 13 | 169 |
| 13 × 14 | 182 |
| 13 × 15 | 195 |
| 13 × 16 | 208 |
| 13 × 17 | 221 |
| 13 × 18 | 234 |
| 13 × 19 | 247 |
| 13 × 20 | 260 |
List of the First 100 Multiples of 13
In order to give you a better understanding of the multiples of 13, we have compiled a list of the first 100 multiples of this number.
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, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533, 546, 559, 572, 585, 598, 611, 624, 637, 650, 663, 676, 689, 702, 715, 728, 741, 754, 767, 780, 793, 806, 819, 832, 845, 858, 871, 884, 897, 910, 923, 936, 949, 962, 975, 988, 1001, 1014, 1027, 1040, 1053, 1066, 1079, 1092, 1105, 1118, 1131, 1144, 1157, 1170, 1183, 1196, 1209, 1222, 1235, 1248, 1261, 1274, 1287, 1300.
Common Multiples of 13 and Other Numbers
The multiples of 13 can also be used to find common multiples of other numbers. For example, if we want to find the common multiples of 13 and 14, we can start by listing out the first few multiples of each number:
13: 13, 26, 39, 52, 65, 78, …
14: 14, 28, 42, 56, 70, 84, …
From this list, we can see that 28 is a common multiple of 13 and 14. This means that 28 is a number that can be divided evenly by both 13 and 14.
Using the LCM to Find Common Multiples
Another way to find common multiples is to use the least common multiple (LCM). The LCM is the smallest multiple that two or more numbers have in common. In other words, it is the smallest number that can be divided evenly by all of the numbers.
To find the LCM of two numbers, we can start by listing out the multiples of each number and finding the smallest one that appears on both lists. In our example of 13 and 14, the LCM is the smallest multiple that appears on both lists, which is 28.
