# What Is the Least Common Multiple of 4 and 3?

## Understanding Common Multiples in Mathematics

Common multiples refer to the multiples shared between a given set of numbers. When we multiply a number by counting numbers, we obtain its multiples. In mathematics, a multiple is the product or result of one number multiplied by another number. We often use multiplication tables to solve math problems, which involve finding multiples. The answer to the multiplication is the multiple of the two numbers.

For instance, let’s consider the multiples of 4:

• 4 times 1 = 4
• 4 times 2 = 8
• 4 times 3 = 12
• 4 times 4 = 16

To better comprehend the concept of multiples, we can rely on multiplication tables representing the first ten multiples of numbers from 1 to 10. An example of a multiples table is displayed below: Now, let’s explore the concept of common multiples through an example. Consider finding the common multiples of 6 and 7. We can list the multiples of 6 and 7 by multiplying them with the numbers 1, 2, 3, and so on.

## Finding Common Multiples of 6 and 7

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 79, 84, …

The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, …

The numbers common to both lists are: 42, 84, …

## Defining Common Multiples

A common multiple is a number that multiple given set of numbers has in common. It refers to the multiples shared between two or more numbers.

## Discovering Common Multiples Between Two Numbers

Finding common multiples between two numbers is simple. We list the multiples of both numbers, then identify the common multiples shared by both lists.

For example, let’s find the common multiples of 6 and 8:

The multiples of 6: 6, 12, 18, 24, 30, 36, …

The multiples of 8: 8, 16, 24, 32, 40, …

The common multiples of 6 and 8: 24, 48, …

## Exploring Common Multiples Between Three Numbers

We can also find the common multiples of three numbers using the listing method. The key is to identify the numbers that are multiples of all three given numbers.

For example, let’s determine the common multiples of 3, 4, and 6:

The multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, …

The multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, …

The multiples of 6: 6, 12, 18, 24, 30, 36, …

The common multiples of 3, 4, and 6: 12, 24, …

## How to Find Common Multiples

To find the common multiples of two or more numbers, we can list the multiples of each number.

Let’s consider finding the common multiples of 6 and 7. We can mark the multiples of 6 and 7 on a hundred grid to visualize them. Multiples of 6 will be marked with a circle, while multiples of 7 will be marked with a cross.

The common multiples of 6 and 7 are the numbers that are both circled and crossed on the grid. In this case, the common multiples are 42 and 84.

Let’s explore one more example:

Example: Find the common multiples of 4 and 12.

Multiples of 4: 4, 8, 12, 16, 20, 24, …

Multiples of 12: 12, 24, 36, 48, 60, 72, …

Common multiples of 4 and 12: 12, 24, …

## Understanding the Least Common Multiple (LCM)

The smallest common multiple among two or more numbers is called the Least Common Multiple (LCM). To find the LCM, we list the multiples of the given numbers and determine their common multiples.

For instance, consider finding the LCM of 3 and 4:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, …

Multiples of 4: 4, 8, 12, 16, 20, 24, …

The common multiples of 3 and 4: 12, 24, …

Therefore, the smallest common multiple is 12, making the LCM of 3 and 4 equal to 12.

## Properties of Common Multiples

• A number can have an infinite number of multiples, resulting in an infinite number of common multiples between any two numbers or sets of numbers.
• For any two numbers, multiplying them together will always yield a common multiple.
• If two numbers are coprime (having no common factors other than 1), their common multiples will be the multiples of their product.
• The LCM of two coprime numbers is equal to the product of the two numbers.
• If one number is a multiple of another, the LCM of the two numbers will be the multiple.

These properties assist in solving problems related to common multiples.

## Practice Problems on Common Multiples

1. What are the multiples of the number 9?
Solution:
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …

2. Find two common multiples of the numbers 2 and 10.
Solution:
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …
The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, …
The two common multiples of 2 and 10 are 10 and 20.

3. Find the LCM of 3 and 5.
Solution:
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, …
The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, …
The common multiples of 3 and 5 are: 15, 30, …
The smallest common multiple is 15, so the LCM of 3 and 5 is 15.

For more practice problems on common multiples, visit 5 WS.

Q: What are the multiples of any given number, such as 9?
A: The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …

Q: Can you provide the common multiples of 2 and 10?
A: The common multiples of 2 and 10 are 10 and 20.

Q: How do you find the LCM of two numbers, like 3 and 5?
A: To find the LCM of 3 and 5, we determine their common multiples, which in this case are 15, 30, … The smallest common multiple is 15, so the LCM of 3 and 5 is 15.

These are some frequently asked questions regarding common multiples.

The 5 Ws and H are questions whose answers are considered basic in information gathering or problem solving. 5ws.wiki will best answer all your questions

### Related Posts ## Daily Checklist for Forklift Safety: What You Need to Know

Forklift trucks are often considered the “heart” of manufacturing operations. It is crucial to ensure the safe and efficient operation of your forklift truck at all times….

## What Does Chicago Think Of Leonid And Friends

Video what does chicago think of leonid and friends A Tale of Resilience: Leonid & Friends and the Ukrainian Crisis Vocalist Serge Tiagnyriadno, a member of the… ## What Happens If You Lose a Car Accident Lawsuit

If you find yourself on the losing end of a car accident lawsuit, the consequences can be daunting. Not only will you be responsible for any damages…

## What Time Does Costco Open For Executive Members

Costco Executive Membership is an exceptional choice for those interested in joining a warehouse club. It provides excellent value for the money, offering a range of perks…

## Days of Our Lives: The Move to Peacock and What You Need to Know

Video what channel is days of our lives on at night If you’re a fan of the long-running soap opera Days of Our Lives and rely on…

## “The Twists and Turns of I Know What You Did Last Summer Episode 6”

Survivors Navigate Danger in Cult Compound In the sixth episode of the thrilling series “I Know What You Did Last Summer,” the remaining members of the O.G….