## Introduction to GCF and LCM Calculator

GCF and LCM calculator is a free online tool that is used to **solve the integer** to find the greatest common factor or least common multiples. It helps you to determine the lcm and gcf of two or more two integers that become the divisors of the given integer.

lcm and gcf calculator is a beneficial tool, especially for students who do not have a tutoring facility and want to learn lcm or gcf concepts on their own. Our calculator for lcm and gcf provides you exact solution as per your number given as an input in a few seconds.

## What are GCF and LCM?

The greatest common factor and least common multiple is the **largest or smallest number** from the common multiple factors. They both have the same method to find the common factors using various types of methods like prime factorization or division method etc.

There is a difference between lcm and gcf is that lcm takes all the common factors and multiplies them to get the least common multiple. On the other hand, gcf only takes the greatest number from the integer common factor.

If the high common factor has repeated numbers like 3,3 then multiply both of them 3*3=9, so 9 is the highest common factor. Using a gcf and lcm calculator can simplify these calculations and ensure accuracy.

## How to Find GCF and LCM Using LCM and GCF Calculator

GCF and LCM are simple and easy methods to solve integers to **find the greatest or lowest common factor** from the given integer. There are numerous methods used to find the lcm and gcf problems, and one efficient way is to you can use our calculator LCM and GCF. These methods are:

## How to Find GCF and LCM Using a Factor Tree

For the factor tree method, a tree is formed where a **given number is written at the top**, and the rest of the factors are multiples of that given number. The least common multiple and greatest common factor calculator uses this method for representation of value

**Step 1**:

When you give an input number in a calculator gcf and lcm, it analyses the given number to find its multiplied

**Step 2**:

It starts finding the multiple from 0 to 9 onward the natural number

**Step 3**:

It arranges all the multiple factors as per the given number and writes it down

**Step 4**:

It writes all the pairs of factors and finds the common multiple.

**Step 5**:

Lastly, gcf lcm finder finds the least common multiple and greatest common factor from the given number.

### Example:

what is the lcm and gcf of 12 and 15

**Solution**:

**For GCF:**

Use the tree factor to find 12 and 15 for gcf

### PASTE THE GRAPH HERE!

$$ Prime\; Factorization\; of\; 12 \;=\; 22 \times 3 $$

$$ Prime\; factorization\; of\; 15 \;=\; 3 \times 5 $$

$$ GCF\; (12,15) \;=\; 3 $$

**For LCM Solution**

**Solution**:

Use the tree factor to find 12 and 15 for Lcm

### PASTE THE GRAPH HERE!

After writing all the common factors we get lcm

$$ All\; the\; common\; factors\; =\; 22 \times 3 \times 5 $$

$$ LCM\; (12,15) \;=\; 60 $$

## How to Find GCF and LCM Using Prime Factorization

The **prime factorization method** is also used to solve both the gcf or lcm problems from the given number.

**For GCF**

Prime factorization is the most common method that helps to find the gcf questions.

**Step 1:**

The calculator writes all the multiple factors of a given number

**Step 2:**

Gcf lcm finder makes a list of all these factors of both numbers.

**Step 3:**

In this step, it uses the factorization method to match all the common factors and find the highest number value.

**Step 4:**

Lastly, the calculator gcf and lcm gives the results as the highest value factor from the common factor is the greatest common factor of the given number.

### Example:

What is the GCF and LCM of 8 and 12

**For GCF Solution**

**Solution**:

Use the prime factor method to find factors of given numbers

$$ The\;Prime\;Factors\;of\;12\;are: 2,2,3 $$

$$ The\;Prime\;Factors\;of\;8\;are:2, 2, 2 $$

$$ Coprime\; numbers\; are\; 2,2 $$

$$ Greatest\; common\; factor \;=\; 2 \times 2 $$

$$ GCF \;=\; 4 $$

**For LCM Solution**

**Solution**:

For a prime factor of 8

$$ 2 \times 2 \times \;=\; 2^3 $$

For a prime factor of 12

$$ 2 \times 2 \times 3 \;=\; 2^2 \times 3^1 $$

Common factor are

$$ 2, 2, 2, 3 $$

Multiply all the common factor

$$ LCM \;=\; 2 \times 2 \times 2 \times 3 \;=\; 24 $$

$$ LCM\;(8, 12) \;=\; 24 $$

## How to Use the GCF and LCM Calculator

The calculator for lcm and gcf has the simplest design that enables you to calculate the integer and get the solution of lcm and gcf instantly. Follow some of our guidelines before you use it and you get an amazing experience every time. These steps are:

**Choose the method**that you want to evaluate to find the common multiple from the given list- Enter the number in the input field of lcm and gcf calculator.
- Review your integer number before clicking on the calculate button so that you get the exact solution without any error in the calculation process.
- Click on the “Calculate” button to get the solution of the gcf or lcm problems
- Click on the “Recalculate” button to get a new page for more evaluation of the integers to get the solution of both the highest or lowest common factors.
- If you want to check the accuracy of the solution then you should first try out the load example and get an accurate solution of lcm and gcf every time.

## Output Obtained from Calculator GCF and LCM

Calculator lcm and gcf gives you a **solution to your given number** value problem after you click on the calculated button. It may include the following:

**Result Option:**

Result option provides you with solutions for both the lcm and gcf factors

**Possible Steps:**

Possible steps provide you with solutions for common multiple calculations in a step-wise process

## Benefits of GCF LCM Calculator

The least common multiple and greatest common factor calculator provide you with tons of benefits whenever you use them to calculate the integer number to find the common factor.

These benefits will make this tool more attractive for everyone who uses it for better learning about LCM and GCF concepts. These benefits are:

- GCF and LCM Calculator with steps save the time and energy that you consume while finding the common multiple for both the greatest or lowest factor manually.
- Our gcf lcm finder is a handy tool that can be operated through a computer, laptop, or mobile easily
- Gcd and lcm calculator has a
**user-friendly interface**so that you can use it to solve integer number problems. - It provides accurate results as per your given input numbers to find the least common multiple or greatest common factor value every time without any mankind of mistake.
- Calculator for lcm and gcf is an educational tool that gives you solutions in the step-by-step method that help you to find the lcm or gcf problem