# Multiples of 30

Created by: Team Maths - Examples.com, Last Updated: May 27, 2024

## Multiples of 30

In mathematics, multiples of 30 are the products obtained by multiplying 30 by integers. These numbers play a crucial role in understanding various concepts such as multiplication, divisors, and factors. A multiple of 30 is any number that can be expressed as 30n, where ‘n’ is an integer. Multiples of 30 include numbers like 30, 60, 90, and so on, each sharing common factors with 30. Understanding multiples helps in solving problems related to number theory and arithmetic operations.

## What are Multiples of 30?

Multiples of 30 are the products obtained by multiplying 30 by any integer. Examples include 30, 60, 90, 120, and so on. These numbers follow the pattern 30n, where n is any integer.

Prime Factorization of 30: 2 × 3 × 5 First 10 Multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300.

Table of 30

## Important Notes

Definition: A multiple of 30 is any number that can be expressed as 30×n, where n is an integer. This means that the multiples of 30 include numbers like 30, 60, 90, 120, and so on.

Common Factors: Multiples of 30 have common factors of 1, 2, 3, 5, 6, 10, 15, and 30. This is because 30 is the product of its prime factors 2×3×5.

Divisibility: A number is a multiple of 30 if it is divisible by both 3 and 10. To check for divisibility by 3, the sum of the digits should be divisible by 3. To check for divisibility by 10, the number must end in 0.

Pattern: The multiples of 30 follow a simple pattern where each multiple increases by 30. For example, starting from 30, the sequence is 30, 60, 90, 120, 150, etc.

Applications: Multiples of 30 are used in various practical applications such as time (minutes in an hour), measurements, and in contexts where grouping or scheduling occurs in intervals of 30 units.

## Examples on Multiples of 30

• 1 × 30 = 30
• 2 × 30 = 60
• 3 × 30 = 90

### Larger Multiples

• 10 × 30 = 300
• 20 × 30 = 600

### Real-Life Examples

• Time: 60 minutes in an hour is a multiple of 30 because 2 × 30 = 60.
• Money: \$30 is a multiple of 30 because 1 × 30 = 30.
• Weight: 300 grams is a multiple of 30 because 10 × 30 = 300.

## Practical Examples of Multiples of 30

### What is the 5th multiple of 30?

The 5th multiple of 30 is 5 × 30 = 150.

### Is 90 a multiple of 30?

Yes, 90 is a multiple of 30 because 3 × 30 = 90.

### What is the next multiple of 30 after 150?

The next multiple of 30 after 150 is 150 + 30 = 180.

### Find the 8th multiple of 30.

The 8th multiple of 30 is 8 × 30 = 240.

### Is 85 a multiple of 30?

No, 85 is not a multiple of 30 because it cannot be expressed as 30 × n where n is an integer.

## What is a multiple of 30?

A multiple of 30 is any number that can be expressed as 30 times an integer, such as 30, 60, 90, etc.

## A multiple of 30 is any number that can be expressed as 30 times an integer, such as 30, 60, 90, etc.

A number is a multiple of 30 if it is divisible by both 2, 3, and 5, since 30 = 2 × 3 × 5.

## What is the smallest positive multiple of 30?

The smallest positive multiple of 30 is 30 itself (30 × 1 = 30).

## What is the 10th multiple of 30?

The 10th multiple of 30 is 30 × 10 = 300.

## Is 150 a multiple of 30?

Yes, 150 is a multiple of 30 because 30 × 5 = 150.

## What is the next multiple of 30 after 300?

The next multiple of 30 after 300 is 300 + 30 = 330.

## Are all multiples of 30 also multiples of 10?

Yes, all multiples of 30 are also multiples of 10 because 30 is a multiple of 10.

## What is the least common multiple (LCM) of 30 and 45?

The least common multiple (LCM) of 30 and 45 is 90.

## Is 200 a multiple of 30?

No, 200 is not a multiple of 30 because it cannot be expressed as 30 × n for any integer n.

## How do you find the common multiples of 30 and another number, such as 50?

To find the common multiples of 30 and 50, you can calculate their least common multiple (LCM). For 30 and 50, the LCM is 150. Therefore, common multiples are 150, 300, 450, etc.

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