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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 2nd multiple by repeated addition, we will add another 15 to 15. Thus,  . Therefore, 30 is the 2nd multiple of 15.

Since we already know that the 2nd multiple of 15 is 30, we will use that knowledge to determine the 3rd multiple. Hence,  . This is also the same as saying  .

Now, if we continue doing this process to get the 5th 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 4th multiple of 15, by repeated addition, we can do this by doing . But by getting the product of 15 and 4, we will have  . Both methods will have the same result, it’s just a matter of choice for you!
Let’s try finding the 17th 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  . Therefore, the 17th 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.

nth Multiple

Repeated Addition

Multiplication

1st multiple

15

2nd multiple

15 + 15 = 30

3rd multiple

15 + 15 + 15 = 45

4th multiple

15 + 15 + 15 + 15 = 60

5th multiple

15 + 15 + 15 + 15 + 15 = 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 2nd 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 78th multiple of 15. So, we will simply get the product of $15 and 78 weeks. Thus, .

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 12th multiple of 15. So,  .

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!

Take a Quiz

Which of the following is a multiple of 15?
a. 950
b. 955
c. 960
d. 965


What is the 13th multiple of 15?
a. 180
b. 195
c. 210
d. 225


Abigail enrolled in guitar lessons that cost $15 per session. If she is registered for 35 sessions, how much did she pay to enroll in guitar lessons?
a. 515
b. 525
c. 535
d. 545

Frequently Asked Questions

To find the nth multiple of 15, we must multiply 15 by any number.

No. Not all numbers that have a units digit of 5 or 0 are a multiple of 15 – such as 5, 10, 20, 25, etc. However, all multiples of 15 end at either 5 or 0.

The 15th multiple of 15 is 225.

The first five multiples of 15 are 15, 30, 45, 60, and 75.

Yes, a multiple of 15 can also be negative.

No, not all multiples of 5 are multiples of 15. However, if a number is both a multiple of 5 and 3, then we can say that it is a multiple of 15.

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