# Multiples of 15

Created by: Team Maths - Examples.com, Last Updated: May 22, 2024

## Multiples of 15

Multiples of 15 are numbers that can be expressed as the product of 15 and an integer. These numbers arise from multiplying 15 by whole numbers, resulting in a sequence like 15, 30, 45, and so on. In mathematics, these multiples are important as they share common factors and divisors, particularly 1, 3, 5, and 15. Understanding multiples helps in solving problems involving factors and divisors, and is fundamental in arithmetic and number theory. Identifying multiples of 15 also simplifies calculations involving larger numbers and their properties.

## What are Multiples of 15?

Multiples of 15 are numbers that result from multiplying 15 by any integer. They form a sequence like 15, 30, 45, 60, and so on. Each multiple of 15 can be expressed as 15n, where n is an integer.

Prime Factorization of 15: 15 = 3 × 5 First 10 multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150.

Table of 15

## Important Notes

Definition of Multiples:

• A number is a multiple of another if, when divided, it results in an integer (i.e., no remainder).

Divisibility Rule for 15:

• A number is divisible by 15 if it is divisible by both 3 and 5.

Examples of Multiples:

45, 90, 105, 135:

Each of these numbers, when divided by 15, results in an integer and has a remainder of 0.

• 45÷15 = 3
• 90÷15 = 6
• 105÷15 = 7
• 135÷15 = 9

Non-Multiple Example:

178:

• When 178 is divided by 15, the result is not an integer.
• 178÷15 = 11.87
• The remainder is 13.

Calculation of Remainders:

• To determine if a number is a multiple of 15, perform the division and check the remainder.
• If the remainder is 0, the number is a multiple of 15.
• If the remainder is not 0, the number is not a multiple of 15.

## Examples on Multiples of 15

### Example 1: 60

• Calculation: 60÷15 = 4
• Reason: 60 divided by 15 equals 4, which is an integer. Therefore, 60 is a multiple of 15.
• Remainder: 0

### Example 2: 150

• Calculation: 150÷15 = 10
• Reason: 150 divided by 15 equals 10, which is an integer. Therefore, 150 is a multiple of 15.
• Remainder: 0

### Example 3: 225

• Calculation: 225÷15 = 15
• Reason: 225 divided by 15 equals 15, which is an integer. Therefore, 225 is a multiple of 15.
• Remainder: 0

## What is a multiple of 15?

A multiple of 15 is any number that can be expressed as 15×n, where n is an integer. Examples include 15, 30, 45, etc.

## How can you determine if a number is a multiple of 15?

To determine if a number is a multiple of 15, divide the number by 15. If the result is an integer with no remainder, the number is a multiple of 15.

## Are all multiples of 15 also multiples of 3 and 5?

Yes, since 15 itself is a product of 3 and 5, all multiples of 15 are also multiples of both 3 and 5.

## What is the smallest positive multiple of 15?

The smallest positive multiple of 15 is 15 itself.

## Is 0 a multiple of 15?

Yes, 0 is a multiple of 15 because 15×0 = 0.

## Can a negative number be a multiple of 15?

Yes, negative numbers can be multiples of 15. For example, -15, -30, and -45 are all multiples of 15.

## What are the first five positive multiples of 15?

The first five positive multiples of 15 are 15, 30, 45, 60, and 75.

## Is 150 a multiple of 15?

Yes, 150 is a multiple of 15 because 150÷15 = 10, which is an integer.

## Is 100 a multiple of 15?

No, 100 is not a multiple of 15 because 100÷15 = 6.67, which is not an integer.

## How do multiples of 15 relate to the LCM and GCD of numbers?

Multiples of 15 are useful in finding the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of numbers. For instance, the LCM of 15 and any other number must be a multiple of 15, and the GCD of 15 with another number often relates to common factors including 15.

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