What are the Multiples of 18?
The multiples of 18 are the numbers obtained on multiplying 18 by any natural number. Consider the number 54. The number 54 is the product of 18 and 3. Hence, 54 is a multiple of 18. Similarly, 18, 36, 54, 72, 90, 108, and so on are multiples of 18.
The multiples of 18 can be generalized as 18n, where n is any natural number. In simple words, the product of 18 and n gives us different multiples.
We get different multiples by selecting different values of n.
When n = 1, 18n = 18
When n = 2, 18n = 36
When n = 3, 18n = 54
When n = 4, 18n = 72
Since the value of n can have an infinite number of values, we can say that 18 has infinitely many multiples. The multiples of 18 can be represented on a number line as follows:
We can observe a pattern among the multiples of 18 on the number line. The multiples of 18 are a series of jumps on the number line. This is due to the fact that multiplication is the same as repeated addition. In fact, multiplication is a math operation used to simplify repeated addition. Since multiples of 18 represent a repeated addition of 18 with itself, the multiples of 18 on a number line are spaced out by 18 divisions. In other words, the difference between two successive multiples of 18 is 18.
Times Table of 18
The multiples of 18 can be arranged in a table known as the times table of 18.
The times table 18 can be extended up to any desired value of n.
Finding Multiples of 18 by Repeated Addition
As we have already discussed, multiplication is a mathematical operation used to simplify repeated addition. We can easily solve math problems involving repeated addition by memorizing the times table of numbers. But the times table of numbers is built upon the concept of repeated addition. So, we need to have an understanding of repeated addition to learn the times table of any number.
Here, we can see that the number 18 is added repeatedly to find its multiples. We will get the value of nth multiple of 18, that is, 18n by adding 18 n times.
Solved Multiples of 18 Examples
Example 1: Is 198 a multiple of 18?
Solution:
198 is a multiple of 18. We get 198 by multiplying 18 by 11. In other words, we get 198 if we add 18, 11 times.
Example 2: What is the 15th multiple of 18?
Solution:
We can find the value of the 15th multiple of 18 by finding 18 \(\times\) 15, or by adding the number 18 fifteen times.
18 \(\times\) 15 = 270
So, the 15th multiple of 18 is 270.
Example 3: Find the lowest common multiple (LCM) of 18 and 9.
Solution:
The multiples of 9 are 9, 18, 27, 36, and so on.
The multiples of 18 are 18, 36, 54, and so on.
Hence, the lowest common multiple of 18 and 9 is 18.
Example 4: The road connecting town A and town B is marked by milestones placed 18 miles apart. If Anne crossed 28 such milestones while traveling from A to B, find the distance between the two towns.
Solution:
Number of milestones between A and B = 28
Distance between each milestone = 18 miles
So, the distance between A and B is the 28th multiple of 18.
Distance between A and B = 18 \(\times\) 28 = 504
Therefore, the distance between the two towns is 504 miles.
Example 5: A cyclist travels 18 miles in an hour. How many miles will the person cover in 4 hours with the same pace?
Solution:
Distance covered in an hour = 18 miles
Distance covered in 4 hours can be calculated by finding the 4th multiple of 18 miles.
Distance covered in 4 hours = 18 \(\times\) 4 = 72
So, the cyclist covers 72 miles in 4 hours.
Multiples are numbers obtained by multiplying two numbers. For example, the multiples of 5 are 5, 10, 15, 20, 25 and so on.
The first ten positive multiples of 18 are 18, 36, 54, 72, 90, 108, 126, 144, 162 and 180.
All numbers, including 18, have an infinite number of multiples.
The 18th multiple of 18 is 324. Since 18 is multiplied by itself to get 324, the number 324 is known as the square of 18.
The multiples of 18 between 100 and 150 are 108, 126 and 144.