Multiples of 18

Posted on07 February 2022

Eighteen is a composite number having divisors of 1, 2, 3, 6, and 9. It is considered a semi-perfect number because its three divisions (3, 6, and 9) have a sum of 18. It is also considered as a lucky number in Chinese because it is pronounced as 十八 (shíbā) which is similar to 實發 (shì fā) which means “to definitely get rich.”

In the Philippines, 18 is the age of maturity. More so, most girls are also excited to celebrate their debut. Usually, the debutante will have her 18 dances, 18 candles from her friends to receive birthday wishes, and 18 bluebills (or thousand peso bills) from her godparents.

Now, are you ready to take a flight towards the exciting world of 18 and its multiple?
Let’s enter the “lucky” and “mature” age of 18!

Multiples of 18 are 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198

A multiple is defined as the product of any quantity with an integer. Thus, to say that any number is a multiple of 18, it should be a product of any integer and 18. In a nutshell, a number that can be expressed as 18n, where n is an integer, is a multiple of 18.

A number is said to be a multiple of 18 if it can be divided or multiplied by 18 and result in a whole number. A sequence of multiples of 18 is a series of numbers in which the difference between two consecutive numbers is always 18. Let’s look at the sequence of numbers below:

18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198

The sequence of numbers above perfectly shows that multiples of 18 will always have a difference of 18 between any two consecutive numbers.

How to find the multiples of 18?

We can find any multiples of 15 by using repeated addition and multiplication.
We simply add 18 as many times as necessary when doing repeated addition. To find multiples of 18 by repeated addition, we shall take note of the first multiple of 18 – which is 18 itself.

Then, in order to get the second multiple, we will add another 18. Thus, 18 + 18 = 36. As a result, we now know that 36 is the second multiple of 18.

So, to find the 5^th multiple of 18 by repeated addition, we will repeatedly add 18 like:

18 + 18 + 18 + 18 + 18 = 90.

Let's have a look at the diagram below to show how simple it is to get multiples of 18 using repeated addition.

As you may have noticed, consecutive multiples of 18 provide a number sequence with a difference of 18 between two consecutive numbers.

It’s not hard to find multiples of 18 using repeated addition, right? Now, let’s try another method which is multiplication!

Say, for example, we are asked to get the 7^th multiple of 18, by repeated addition, we can do this by doing

18 + 18 + 18 + 18 + 18 + 18 + 18 = 126. However, if we get the product of 18 and 7, we will simply have

$1\mathbf8\boldsymbol\;\boldsymbol\times\boldsymbol\;\mathbf7\boldsymbol\;\boldsymbol=\boldsymbol\;\mathbf{126}$ .

Hence, the 7^th multiple of 18 is 126. Multiplication method is an easier way to find multiples of 18.

Now, how about finding the 51^st multiple of 18? Multiplying 18 by 51 will give us

$\mathbf{18}\boldsymbol\;\boldsymbol\times\boldsymbol\;\mathbf{51}\boldsymbol\;\boldsymbol=\boldsymbol\;\mathbf{918}$ .

Therefore, the 51^st multiple of 18 is 918.

Let’s look at the table below. The table shows the first five multiples of 18 and how we can find them using repeated addition and multiplication method.

n^th Multiple	Repeated Addition	Multiplication
1^st multiple	18	$18\;\times\;1\;=\;18$
2^nd multiple	18 + 18 = 36	$18\;\times\;2\;=\;36$
3^rd multiple	18 + 18 + 18 = 54	$18\;\times\;3\;=\;54$
4^th multiple	18 + 18 + 18 + 18 = 72	$18\times\;4\;=\;72$
5^th multiple	18 + 18 + 18 + 18 + 18 = 90	$18\;\times\;5\;=\;90$

Awesome! You can now quickly find any multiples of 18.

Did you know that…
The numerical value of the Hebrew word "chai," which means "life," is eighteen. It's a deceptively simple two-letter word composed of the Hebrew letters "chet" and "yud." In Jewish tradition, it is a ritual to give monetary gifts in multiples of 18 – which means the receiver is being blessed with long life. Hence, the reason for Jews to give donations and presents in increments of 18 such as 18, 36, 54, 72, 180, 360, 1800, and so on.

List of First 30 multiples of 18

Since there is an infinite amount of integers, listing all possible multiples of 18 is meaningless. Hence, the idea of putting only the first 30 possible multiples of 18 is to verify if you will have the same result of getting the first 30 multiples of 18. Thus, to list the first 30 multiples of 18, we must multiply the numbers 1-30 by 18.

Product of 18 and a positive counting number	Multiples of 18
$18\times\;1$	18
$18\times\;2$	36
$18\times\;3$	54
$18\times\;4$	72
$18\times\;5$	90
$18\times\;6$	108
$18\times\;7$	126
$18\times\;8$	144
$18\times\;9$	162
$18\times\;10$	180
$18\times\;11$	198
$18\times\;12$	216
$18\times\;13$	234
$18\times\;14$	252
$18\times\;15$	270
$18\times\;16$	288
$18\times\;17$	306
$18\times\;18$	324
$18\times\;19$	342
$18\times\;20$	360
$18\times\;21$	378
$18\times\;22$	396
$18\times\;23$	414
$18\times\;24$	432
$18\times\;25$	450
$18\times\;26$	468
$18\times\;27$	486
$18\times\;28$	504
$18\times\;29$	522
$18\times\;30$	540

Solving problems involving multiples of 18

There are some instances where we unconsciously apply our knowledge to solve reallife problems involving multiples of 18. Let’s try to solve some of these problems!

Problem #1
Khristian bought gifts for his friends that cost $18 each. If he had to buy 15 gifts for his friends, how much did he spend on buying gifts?

To find the total amount Khristian spends on buying gifts for his friends, we should take note of the fact that each gift costs $18. Since Khristian bought 15 gifts for his 15 friends, we can get the total amount he spent by getting the 15^th multiple of 18.

Hence, this will lead us to get the product of $18 and 15.

Thus, $\boldsymbol\$\mathbf{18}\boldsymbol\;\boldsymbol\times\boldsymbol\;\mathbf{15}\boldsymbol\;\boldsymbol=\boldsymbol\;\boldsymbol\$\mathbf{270}$ .

Therefore, Khristian spent $270 on buying gifts for his 15 friends. Khristian is such a generous and thoughtful friend.

Now, let’s try another problem.

Problem #2
Emmylou dreams of becoming a professional surfer, so she allots 18 hours a week to practice dancing in the waves. If there are 52 weeks in a year, how many number of hours did she spend surfing?

In the given problem, it is stated that Emmylou spends 18 hours a week practicing surfing. Now, we are asked to determine the total number of hours she spent surfing in a year. For us to solve the problem, we should take note of the fact that there are 52 weeks in a year.

Hence, $\mathbf{18}\boldsymbol\;\mathbf{hours}\boldsymbol\;\boldsymbol\times\boldsymbol\;\mathbf{52}\boldsymbol\;\mathbf{weeks}\boldsymbol\;\boldsymbol=\boldsymbol\;\mathbf{936}\boldsymbol\;\mathbf{hours}$ .