# Multiples of 15

**Fifteen** is the middle number between 10 and 20. It is also a number that comes after 14 and before 16. Fifteen is a composite number where its proper divisors are 1, 3, and 5.

Fifteen is a special number, especially in countries in Latin America such Colombia, Cuba, Ecuador, Venezuela, and Peru. This is because of their **quinceañera** – which is a celebration when a girl becomes 15 years old. For them, fifteen marks the day that little princesses transition to womanhood.

Fifteen is such an important and meaningful number. Even Taylor Swift said that if you are and somebody tells you they love you, you just have to believe it! Now, let’s learn more about this number and its multiple. Are you ready?

## Multiples of 15 are 15, 30, 45, 60, 75, 90, 105

If a number can be divided or multiplied by 15, resulting in a whole number, we can say that that is a multiple of 15. The numbers that are *n*-times of 15 produced numbers that are multiples of 15, where *n* = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10… and so on. In short, multiples of 15 are numbers that can be expressed as* 15n* where

*n*is any integer.

A sequence of numbers where the difference between two consecutive numbers is always 15 is a sequence of multiples of 15.

Did you notice that the difference between any two consecutive numbers is always 15? Thus, we can say that the numbers in the sequence are all multiples of 15!

## How to Find the Multiples of 15?

**Repeated addition** and **multiplication** are two methods that we can use to find any multiples of 15.

As the name suggests, **repeated addition** is done by repeatedly adding 15 as many times as necessary. To determine multiples of 15 by repeated addition, we will start the process by determining the first multiple of 15 – which is 15 itself. Hence, to get the 2^{nd} multiple by repeated addition, we will add another 15 to 15. Thus, $$15 + 15 = 30$$ . Therefore, 30 is the 2^{nd} multiple of 15.

Since we already know that the 2^{nd} multiple of 15 is 30, we will use that knowledge to determine the 3^{rd} multiple. Hence, $$30 + 15 = 45$$ . This is also the same as saying $$15\;+\;15\;+\;15\;=\;45$$ .

Now, if we continue doing this process to get the 5^{th} multiple of 15, we should have the same result as shown in the diagram.

It’s so simple and straightforward, isn’t it?

Now, let’s try a more simple method. We have defined a multiple of 15 as a product of 15 and any integer. Hence, the alternative method we can use to determine any multiples of 15 is by **multiplication**!

For example, we are asked to get the 4^{th} multiple of 15, by repeated addition, we can do this by doing $$15\;+\;15\;+\;15\;+\;15\;=\;60$$ . But by getting the product of 15 and 4, we will have $$15\times4\;=\;60$$ . Both methods will have the same result, it’s just a matter of choice for you!

Let’s try finding the 17^{th} multiple of 15. If we use repeated addition, it will take us some time before we get the answer. Using the multiplication method, we can easily have $$15\;\times\;17\;=\;255$$ . Therefore, the 17^{th} multiple of 15 is 255.

Observe the table below. We’ve listed the first five multiples of 15 and how we can find it using repeated addition and multiplication method.

n |
Repeated Addition |
Multiplication |
---|---|---|

1 |
15 |
$$15\;\times\;1\;=\;15$$ |

2 |
15 + 15 = 30 |
$$15\;\times\;2\;=\;30$$ |

3 |
15 + 15 + 15 = 45 |
$$15\;\times\;3\;=\;45$$ |

4 |
15 + 15 + 15 + 15 = 60 |
$$15\;\times\;4\;=\;60$$ |

5 |
15 + 15 + 15 + 15 + 15 = 75 |
$$15\;\times\;5\;=\;75$$ |

## Did you know that…

The number 15 is a triangular number?

A triangular number is a number that forms an equilateral if they are represented through dots and arranged in a triangle. Triangular numbers are the sum of consecutive numbers. Say, in 15, if we get the sum of 1, 2, 3, 4, and 5, we will have **1 + 2 + 3 + 4 + 5 = 15 **.

Observe that the triangle we made has five dots on the bottom, five on the right, and five on the left.

What a fantastic discovery, huh? Now, can you guess what is the next triangular number?

## List of First 30 Multiples of 15

To make the list of the first 30 multiples of 15, we simply get the product of 15 and a positive counting number. We start by multiplying 15 by 1 to obtain the first multiply of 15 – which is 15. Then, multiply 15 by 2 to get the 2^{nd} multiple, and so on. Listing all of the possible multiples of 15 is pointless as there is an unlimited number of integers.

Product of 15 and a positive counting number | Multiples of 15 |
---|---|

15 x 1 |
15 |

15 x 2 |
30 |

15 x 3 |
45 |

15 x 4 |
60 |

15 x 5 |
75 |

15 x 6 |
90 |

15 x 7 |
105 |

15 x 8 |
120 |

15 x 9 |
135 |

15 x 10 |
150 |

15 x 11 |
165 |

15 x 12 |
180 |

15 x 13 |
195 |

15 x 14 |
210 |

15 x 15 |
225 |

15 x 16 |
240 |

15 x 17 |
255 |

15 x 18 |
270 |

15 x 19 |
285 |

15 x 20 |
300 |

15 x 21 |
315 |

15 x 22 |
330 |

15 x 23 |
345 |

15 x 24 |
360 |

15 x 25 |
375 |

15 x 26 |
390 |

15 x 27 |
405 |

15 x 28 |
420 |

15 x 29 |
435 |

15 x 30 |
450 |

Do you observe something? The units digit of any multiple of 15 always ends at 5 or 0!

## Solving Problems Involving Multiples of 15

Now, let’s try solving these two real-life problems about multiples of 15.

**Problem #1**

Ruth saves $15 every week. How much money did she save after 78 weeks?

The problem states that Ruth saves $15 each week, and we are asked to get the total amount of money she saved up for 78 weeks. Hence, to get the total money she saves, we need to find the 78^{th} multiple of 15. So, we will simply get the product of $15 and 78 weeks. Thus, **$$\$15\;\times\;78\;=\;\$1,170$$** .

Therefore, Ruth saved a total of **$1,170** in 78 weeks!

Let’s try another one.

**Problem #2**

Camila pays $15 every month for her reading subscription. What is the total amount of money that she needs to pay in 1 year?

To solve for the total amount Camila pays for her reading subscription, we must note that $15 is her monthly payment. We know that there are 12 months in a year. Hence, we need to get the 12^{th} multiple of 15. So, **$$\$15\;\times\;12\;months\;=\;\$180$$** .

Therefore, Camila needs to pay **$180** for her reading subscription.

See… solving problems about multiples of 15 is not as hard as you think it would be! Now, let’s practice everything we’ve learned today and put ourselves into a challenge by answering these three short questions!