# Multiples of 18

Created by: Team Maths - Examples.com, Last Updated: May 23, 2024

## Multiples of 18

Multiples of 18 are numbers that result from multiplying 18 by any integer. In mathematics, a multiple is the product of a given number and an integer. The concept of multiples is closely related to the ideas of factors and divisors, where factors of 18 are numbers that divide 18 exactly without leaving a remainder. Understanding multiples of 18 helps in various arithmetic operations, including finding common multiples and solving problems involving division and multiplication. These multiples are integral in number theory and have applications in many areas of mathematics.

## What are Multiples of 18?

Multiples of 18 are the numbers you get when you multiply 18 by any integer. Examples include 18, 36, 54, 72, and so on. These multiples are essential in understanding arithmetic operations involving division and multiplication.

Prime Factorization of 18: 18 = 2 × 3² First 10 multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180.

Table of 18

## Important Notes

Definition: Multiples of 18 are the numbers that you get when you multiply 18 by any integer. These numbers are part of the arithmetic sequence where each term is 18 units apart.

Examples: Some common multiples of 18 include 18, 36, 54, 72, 90, and so on. Each of these is the result of 18×n, where n is an integer.

Identification: To determine if a number is a multiple of 18, divide the number by 18. If the result is an integer without any remainder, then the number is a multiple of 18.

Relationship to Factors: Factors of 18 (1, 2, 3, 6, 9, 18) are numbers that divide 18 exactly. Multiples of 18, on the other hand, are numbers that 18 divides exactly.

Applications: Multiples of 18 are useful in solving problems related to common multiples, least common multiples (LCM), and in various arithmetic operations involving division and multiplication.

Pattern: Multiples of 18 follow a consistent pattern in arithmetic sequences. They can be generated by repeatedly adding 18 to the previous multiple.

Divisibility: A number is divisible by 18 if it is divisible by both 2 and 9. This is because 18 is the product of these two prime factors (2×9 = 18).

## Examples on Multiples of 18

### First 10 Multiples of 18:

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

• 18×1 = 18
• 18×2 = 36
• 18×3 = 54
• 18×4 = 72
• 18×5 = 90
• 18×6 = 108
• 18×7 = 126
• 18×8 = 144
• 18×9 = 162
• 18×10 = 180

### Real-World Example:

• If you have 18 apples and you want to distribute them equally among different groups, any group size that is a multiple of 18 (e.g., 36, 54) will work perfectly without leaving any apples behind.

### Example 1: Is 54 a multiple of 18?

• Calculation: 54÷18 = 3
• Result: Yes, because the quotient is an integer.

### Example 2: Is 100 a multiple of 18?

• Calculation: 100÷18 = 5.555…
• Result: No, because the quotient is not an integer.

### Common Multiples:

Example: Find the least common multiple (LCM) of 18 and 24.

• Multiples of 18: 18, 36, 54, 72, 90, 108, …
• Multiples of 24: 24, 48, 72, 96, 120, …
• LCM: 72

## What is a multiple of 18?

A multiple of 18 is any number that can be expressed as 18 times an integer. For example, 18, 36, 54, and 72 are all multiples of 18.

## How do you determine if a number is a multiple of 18?

To determine if a number is a multiple of 18, divide the number by 18. If the result is an integer with no remainder, the number is a multiple of 18.

## What are the first five multiples of 18?

The first five multiples of 18 are 18, 36, 54, 72, and 90.

## Is 108 a multiple of 18?

Yes, 108 is a multiple of 18 because 108÷18 = 6, which is an integer.

## Can negative numbers be multiples of 18?

Yes, negative numbers can be multiples of 18. For example, -18, -36, and -54 are all multiples of 18.

## What is the 10th multiple of 18?

The 10th multiple of 18 is calculated by 18×10 = 180.

## Is 200 a multiple of 18?

No, 200 is not a multiple of 18 because 200÷18 = 11.11, which is not an integer.

## How are multiples of 18 used in real life?

Multiples of 18 can be used in various real-life scenarios, such as organizing events, packaging items in groups, and solving problems in number theory and arithmetic.

## What is the smallest positive multiple of 18?

The smallest positive multiple of 18 is 18 itself.

## Are all multiples of 18 also multiples of 9?

Yes, all multiples of 18 are also multiples of 9 because 18 is a multiple of 9 (18 = 9×2). Therefore, any multiple of 18 will also be divisible by 9.

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