# Multiples of 27

Created by: Team Maths - Examples.com, Last Updated: May 24, 2024

## Multiples of 27

Multiples of 27 are integers obtained by multiplying 27 by any whole number. In mathematics, multiples are numbers that result from multiplying a given number by the set of integers. The number 27 itself is both a factor and a divisor of its multiples. Understanding multiples helps in grasping key concepts like factors, divisors, and multiplication. This knowledge is essential for various mathematical operations and problem-solving.

## What are Multiples of 27?

Multiples of 27 are numbers that can be expressed as 27 times an integer. These numbers follow the sequence 27, 54, 81, 108, and so on. Each multiple results from multiplying 27 by whole numbers: 1, 2, 3, 4, etc.

Prime factorization of 27: 27 = 3 × 3 × 3 = 3³ First 10 multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243 270.

Table of 27

## Important Notes

### Definition

• Multiples of 27 are numbers that can be expressed as 27 times an integer.
• The sequence starts from 27 and increases by 27 each time (i.e., 27, 54, 81, 108, etc.).

### 2. Pattern and Sequence

• The sequence of multiples of 27 is arithmetic, with a common difference of 27.
• Formula to find the n-th multiple: 27n where n is a positive integer.

### 3. First 10 Multiples

• The first 10 multiples of 27 are: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270.

### 4. Properties

• All multiples of 27 are divisible by 27.
• They are also multiples of 3 and 9, as 27 is a multiple of both.

### 5. Applications

• Common multiples: When finding common multiples with another number, such as in least common multiple (LCM) calculations.
• Real-life examples: Situations involving grouping or partitioning into 27 parts, such as packaging or distributing items.

## Examples on Multiples of 27

### Example 1: Finding Multiples in a Range

Problem: Identify all multiples of 27 between 100 and 500.

Start with the smallest multiple of 27 greater than or equal to 100.

27×4 = 108

Continue finding subsequent multiples of 27 until reaching or exceeding 500.

• 27×5 = 135
• 27×6 = 162
• 27×7 = 189
• 27×8 = 216
• 27×9 = 243
• 27×10 = 270
• 27×11 = 297
• 27×12 = 324
• 27×13 = 351
• 27×14 = 378
• 27×15 = 405
• 27×16 = 432
• 27×17 = 459
• 27×18 = 486

Multiples of 27 between 100 and 500: 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486.

### Example 2: Using Multiples to Solve a Word Problem

Problem: A factory produces 27 widgets per hour. How many widgets will the factory produce in an 8-hour workday?

Find the total number of widgets produced in 8 hours by multiplying 27 by 8.

27×8 = 216

The factory will produce 216 widgets in an 8-hour workday.

### Example 3: Determining Common Multiples

Problem: Find the least common multiple (LCM) of 27 and 36.

List the first few multiples of each number:

• Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, …
• Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, …

Identify the smallest common multiple.

Common multiples: 108, 216, 324, …

The least common multiple (LCM) of 27 and 36 is 108.

### Example 4: Using Multiples for Divisibility

Problem: Determine if 405 is a multiple of 27.

Divide 405 by 27.

405÷27 = 15

Since 15 is an integer, 405 is a multiple of 27.

Yes, 405 is a multiple of 27.

### Example 5: Multiples in Sequences

Problem: Find the 12th multiple of 27.

Multiply 27 by 12.

27×12 = 324

The 12th multiple of 27 is 324.

## What are the first five multiples of 27?

The first five multiples of 27 are 27, 54, 81, 108, and 135.

## How do you determine if a number is a multiple of 27?

A number is a multiple of 27 if it can be divided by 27 without leaving a remainder.

## Is 270 a multiple of 27?

Yes, 270 is a multiple of 27 because 270 ÷ 27 = 10.

## What is the 10th multiple of 27?

The 10th multiple of 27 is 270 (27 × 10 = 270).

## Are multiples of 27 always odd?

No, multiples of 27 can be both odd and even. For example, 54 (27 × 2) is even, and 27 is odd.

## What is the least common multiple (LCM) of 27 and 36?

The least common multiple of 27 and 36 is 108.

## How many multiples of 27 are there between 100 and 200?

There are three multiples of 27 between 100 and 200: 108, 135, and 162.

## Can multiples of 27 be negative?

Yes, multiples of 27 can be negative. For example, -27, -54, and -81 are negative multiples of 27.

## What is the 15th multiple of 27?

The 15th multiple of 27 is 405 (27 × 15 = 405).

## Are all multiples of 27 also multiples of 3?

Yes, since 27 is a multiple of 3, all multiples of 27 are also multiples of 3.

Text prompt