How to Find Multiples of 18 Quickly and Accurately
In mathematics, multiple is considered the product of any quantity with an integer. In simpler words, if there are two quantities x and y, we can say that x is the multiple of y if x = ny for some integer n. Here, n is termed as the multiplier. If x is not zero, then it will be equivalent to say that x/y is an integer. It is necessary to be clear with this chapter for understanding the other advanced chapters of mathematics and physics. In this article, we will learn about the multiples of 18.
Overview on Multiples of 18
Multiples of 18 are the numbers that can get divided by 18. These multiples don't leave any remainder when they are divided by 18. The quotient of these multiples, when divided by 18, is always a natural number. The list of 18 multiples is infinite and has no limit. Let's list out some of the multiples to give an overview:
18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252,.........
Many students have the misconception that factors are also multiples, but that is wrong.. Factors of 18 are those numbers that are multiplied together in order to obtain the original number which is 18. Whereas, multiples are the term that is given to the numbers that can be written in the form of np, where n is considered as the series of natural numbers and p is considered as the number of which we need to obtain the multiples. Another important thing to remember regarding multiples is that when the multiples of a number get divided by the original number, then the result obtained comes out to be a whole number. Let us see some examples:
Let's take three multiples of 18: 18, 36, 54
When these three multiples are divided by 18, which is the original number, the results are:
18 ÷ 18 = 1
36 ÷ 18 = 2
54 ÷ 18 = 3
Here 1, 2 and 3 are whole numbers.
What do You Understand by Multiples of 18?
Any number that can be denoted in the form of 18n where n is any natural number or an integer, then that number is considered as a multiple of 18. To give a detailed view, numbers such as 18, 36, 54, 180, 360, 540 are Multiple of 18. The justification is given in the table below:
Justification for Multiples of 18:
The values that are obtained are termed as 18 Multiples because these values are coming out by adding and subtracting the original value many times.
To give a cleared view on this chapter and all Multiple of 18, here are the first 20
Multiples of 18 chart:
How to Find the 9th Multiple of 18?
In order to find the 9th Multiple of 18, a student needs to multiply 18 with 9, which is the required number as we are aiming to obtain the 9th Multiple of 18. In this case, n is considered as 9.
18 × n = 18n
18 × 9 = 162
Therefore, the 9th Multiple of 18 is 162
Suppose a student needs to find the 4th Multiple of 18.
18 × 4 = 72.
Likewise, every Multiple of 18 can be obtained using this formula.
Fun Facts
Zero is considered as the Multiple of every number because when any number is multiplied with zero, the product obtained is also zero. So be it a bigger number or a smaller number, every number has one common multiple which is zero.
Each and every number is multiple in itself. As 18 has more factors than itself and 1, it is considered to be a composite number.
There is not a single number that isn’t a factor in itself. This is because every number is divisible by 1 and so, it also happens to be a factor of itself.
The process of the expression of a particular number as a product of its prime factors is known as prime factorisation.
Solved Problems
1. What is the 3rd Multiple of 18?
Solution: Let consider n as 3 because we are finding out the 3rd multiple
18 × n = 18n
18 × 3 = 54
Therefore the 3rd Multiple of 18 is 54.
2. What is the 6th Multiple of 18?
Solution: The first case- Let's consider n as 6 because we are finding out the 6th multiple.
18 × n = 18n
18 × 6 = 108
Therefore the 6th Multiple is 108.
3. Find the 8th multiple of 38.
Solution: Let’s take n as 8 as we have to find the 8th multiple.
Therefore,
38 x n = 38n
38 x 8 = 304
Therefore, 304 is the 8th multiple of 38.
FAQs on Multiples of 18: Definition, List, and Solved Examples
1. What are the multiples of 18?
A multiple of 18 is any number that can be obtained by multiplying 18 with an integer (like 1, 2, 3, etc.). In other words, if a number can be divided by 18 with no remainder, it is a multiple of 18. For example, 54 is a multiple of 18 because 18 × 3 = 54.
2. How do you find the multiples of 18?
To find the multiples of 18, you simply multiply 18 by the sequence of natural numbers (1, 2, 3, 4, and so on). The product of each multiplication is a multiple. For instance:
- 18 × 1 = 18
- 18 × 2 = 36
- 18 × 3 = 54
This process can be continued to find an infinite list of multiples.
3. What are the first ten multiples of 18?
The first ten multiples of 18 are the results of multiplying 18 by the integers from 1 to 10. The list is as follows: 18, 36, 54, 72, 90, 108, 126, 144, 162, and 180.
4. What is the easiest way to check if a large number is a multiple of 18?
To quickly check if a number is a multiple of 18, you must verify that it is divisible by both 2 and 9 (since 18 = 2 × 9).
- Check for 2: The number must be an even number (its last digit must be 0, 2, 4, 6, or 8).
- Check for 9: The sum of all the digits of the number must be divisible by 9.
If the number passes both these tests, it is a multiple of 18.
5. What is the main difference between the multiples and factors of 18?
The primary difference between multiples and factors of 18 relates to their value and quantity:
- Multiples: These are the results of multiplying 18 by an integer (e.g., 18, 36, 54, ...). Multiples are generally larger than or equal to 18, and there is an infinite number of them.
- Factors: These are the numbers that divide 18 exactly (1, 2, 3, 6, 9, 18). Factors are always less than or equal to 18, and there is a finite, specific set of them.
6. Are all multiples of 18 also multiples of 9? Why?
Yes, every multiple of 18 is also a multiple of 9. This is because 18 itself is a multiple of 9 (since 9 × 2 = 18). Any number that is a multiple of 18 can be written as 18 × n (where 'n' is an integer). This can be rewritten as (9 × 2) × n, which clearly shows that the result will always be divisible by 9. The reverse is not true; for example, 27 is a multiple of 9 but not of 18.
7. Can you give a real-world example of using multiples of 18?
A practical example is in manufacturing or packaging. If a factory packs T-shirts into boxes that each hold 18 shirts, the total number of shirts in any number of full boxes will always be a multiple of 18. To find the total shirts in 5 boxes, you'd calculate the 5th multiple: 18 × 5 = 90 shirts. This concept is useful for inventory, logistics, and scheduling.
8. What is the smallest positive multiple of 18?
The smallest positive multiple of any number is the number itself. This is obtained by multiplying the number by 1. Therefore, the smallest positive multiple of 18 is 18 (18 × 1 = 18).
9. How do you find the first common multiple of 18 and 12?
To find the first common multiple, also known as the Least Common Multiple (LCM), you can list the multiples of each number until you find the first number that appears in both lists.
- Multiples of 18 are: 18, 36, 54, 72, ...
- Multiples of 12 are: 12, 24, 36, 48, ...
The first number to appear in both lists is 36. Thus, 36 is the first common multiple of 18 and 12.
