# Multiples of 45

Created by: Team Maths - Examples.com, Last Updated: May 29, 2024

## Multiples of 45

Multiples of 45 are numbers obtained by multiplying 45 by an integer. In mathematics, these multiples form an arithmetic sequence where each term is a product of 45 and a whole number. Understanding multiples helps in recognizing patterns in numbers, simplifying division problems, and finding common divisors and factors. Multiplication plays a crucial role in identifying these multiples, which include numbers like 45, 90, 135, and so on. Exploring multiples of 45 enhances comprehension of integer properties and number theory concepts.

## What are Multiples of 45?

Multiples of 45 are numbers obtained by multiplying 45 by any integer. These include 45, 90, 135, and so on. Each multiple of 45 has 45 as a common factor and can be divided evenly by 45.

Prime Factorization of 45: 3 × 3 × 5 First 10 Multiples of 45 are 45, 90, 135, 180, 225, 270, 315, 360, 405, 450.

Table of 45

## Important Notes

Definition: Multiples of 45 are numbers that can be expressed as 45 times any integer (e.g., 45, 90, 135).

Sequence: The sequence of multiples of 45 begins with 45, 90, 135, 180, 225, and continues infinitely by adding 45 repeatedly.

Divisibility: Any multiple of 45 is divisible by both 45 and its factors, such as 1, 3, 5, 9, 15, and 45.

Calculation: To find the nth multiple of 45, multiply 45 by n (e.g., the 5th multiple of 45 is 45 x 5 = 225).

Patterns: Multiples of 45 end in either 0 or 5, reflecting the fact that 45 is a multiple of both 5 and 9.

## Examples on Multiples of 45

### Simple Multiples

• 45: 45 × 1 = 45
• 90: 45 × 2 = 90
• 135: 45 × 3 = 135
• 180: 45 × 4 = 180
• 225: 45 × 5 = 225

### Larger Multiples

• 450: 45 × 10 = 450
• 900: 45 × 20 = 900
• 1350: 45 × 30 = 1350
• 1800: 45 × 40 = 1800
• 2250: 45 × 50 = 2250

### Real-Life Examples

• Time: 45 minutes is a multiple of 45 because 45 × 1 = 45.
• Money: \$4.50 (450 cents) is a multiple of 45 because 45 × 10 = 450.
• Measurements: A 45-inch TV screen is a multiple of 45 because 45 × 1 = 45.
• Distance: 45 kilometers is a multiple of 45 because 45 × 1 = 45.
• Weight: 90 pounds is a multiple of 45 because 45 × 2 = 90.

## Practical Examples of Multiples of 45

### What is the 10th multiple of 45?

The 10th multiple of 45 is 45 × 10 = 450.

### Is 135 a multiple of 45?

Yes, 135 is a multiple of 45 because 45 × 3 = 135.

### What is the next multiple of 45 after 180?

The next multiple of 45 after 180 is 180 + 45 = 225.

### Find the 15th multiple of 45.

The 15th multiple of 45 is 45 × 15 = 675.

### Is 500 a multiple of 45?

No, 500 is not a multiple of 45 because it cannot be expressed as 45 × n.

## What are multiples of 45?

Multiples of 45 are numbers that can be evenly divided by 45. They are obtained by multiplying 45 by any integer (positive, negative, or zero). Examples include 45, 90, 135, and 180.

## How do you find the first five multiples of 45?

To find the first five multiples of 45, you multiply 45 by the first five positive integers:
45 × 1 = 45
45 × 2 = 90
45 × 3 = 135
45 × 4 = 180
45 × 5 = 225

## Is 450 a multiple of 45?

Yes, 450 is a multiple of 45. To verify, divide 450 by 45: 450 ÷ 45 = 10
Since the result is an integer, 450 is a multiple of 45.

## What is the smallest multiple of 45?

The smallest multiple of 45 is 45 itself. This is because 45 × 1 = 45.

## Are all multiples of 45 also multiples of 15?

Yes, all multiples of 45 are also multiples of 15. This is because 45 is a multiple of 15 (45 = 15 × 3), so any multiple of 45 will be a multiple of 15.

## What is the 10th multiple of 45?

The 10th multiple of 45 is found by multiplying 45 by 10: 45 × 10 = 450

## Can a negative number be a multiple of 45?

Yes, a negative number can be a multiple of 45. For example, -45, -90, and -135 are all multiples of 45.

## How can you check if a number is a multiple of 45?

To check if a number is a multiple of 45, divide the number by 45. If the result is an integer with no remainder, then the number is a multiple of 45.

## What are the common multiples of 45 and 60?

To find common multiples of 45 and 60, you need to list multiples of both numbers and identify the common ones. The first few common multiples are: 180, 360, 540, etc.

## What is the least common multiple (LCM) of 45 and 75?

The least common multiple (LCM) of 45 and 75 is the smallest number that both 45 and 75 divide into without leaving a remainder. The LCM of 45 and 75 is 225.

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