LCM and GCF: Definition, Formula and How to Find Both?

When calculating LCM and GCF problems side by side, it is normal to become confused. The reason for this is a resemblance in the approach used to investigate and answer both of these topics. Today, we’ll aim to clear up any misconceptions about these terms and show you how to correctly find them without getting stuck in the calculations.

LCM – Definition

The smallest common multiple of two or more numbers is known as the LCM. It is the short form of Least Common Multiple. To put it simply, it is the smallest integer that can be entirely divided by all of the given numbers.

GCF – Definition

GCF is the short form of greatest common factor. It is the greatest number that can divide all of the input numbers. There will be no bigger number that divides two or more identical numbers.

You may need to use a GCF calculator to find these terms in order to achieve the best results. Both of these terms are required for adding or subtracting fractional terms.

We’ll show you how to quickly find the Least Common Multiple and Highest Common factors by using online tools as well as manually.

How to find the lowest and greatest common factors?

You can use the following methods to find GCF and LCM of any number.

1. Prime Factorization Method

Prime Factorization is the simplest technique to find both of these concepts. This strategy makes it relatively simple to comprehend and answer a question. You merely need to follow a few easy procedures and divide integers by a predetermined quantity.

As the method’s name implies, the number will be prime or unique. Prime numbers are numbers that cannot be divided by any other number in mathematics.

In this method, you must divide all of the numbers by a prime number such as 2, 3, or any other number.

Finally, all of those prime factors will be properly multiplied to find the GCF and LCM. It is really simple to follow this procedure to find both of these factors.

However, you may not always be able to apply this strategy as directed by the examiner or teacher. To answer your problems, you may need to utilize a more difficult strategy, such as the division method.

2. Division Method

In comparison to the previous method, this one is more complicated and perplexing. In this scenario, you can utilize the LCM Calculator to get precise answers.

No matter how many phrases are in your data set, you may simply solve it using an online calculator. The only thing you need to concentrate on is adding your numbers.

3. List of Factors/Multiples Method

The list of factors method is another way to find the least common multiple and greatest common factor of numbers. In this method, we write down all factors of every number and choose the highest common number in all of the factors of each number.

In the case of LCM, list the multiples of each number instead of listing factors. Then, find the least common number in the multiples of each number.

Let’s take a quick look at how you can use a tool to find GCF and LCM.

In this section, we will go over each method for calculating LCM and GCF with an online calculator one by one. To acquire the correct answer, you only need to master this approach and input your data appropriately.

To begin, use your search browser to look up the LCM Calculator. Such products offer a straightforward user interface, with each section clearly identified.

You simply need to input all of the digits in the provided area. Keep in mind that commas (,) must be used between two numbers. If you do not do this, the tool will treat all of your numbers as a single number and report faults.

After that, all you have to do is click the “Calculate” button. The utility will run many commands on your data to obtain the correct answer.

Furthermore, the whole solution to the problem will be displayed on your screen. You can also understand how the tool handled the problem and try to become an expert in the topic on your own.

When checking for HCF of different numbers, there isn’t much of a difference. To complete this task, you simply need to use the greatest common factor calculator.

It will collect data from you in the same manner as described before. The only difference will be in how commands are implemented.

Also, the results displaying manner will alter slightly from the LCM calculator. You may also be able to verify the whole solution to your query to make a note of it in any of your preferred locations.

Because of this feature, many students use this calculator to finish their homework.

Where do we use LCM and GCF?

LCM and GCF can be used for several purposes in mathematics. Here’s a few of the applications of greatest common factor and least common multiple.

Adding fractional terms

In elementary mathematics, you must add or subtract distinct fractional terms.

You can’t finish this operation unless you take the LCM of the denominators of all fractions. Without properly taking LCM, a fractional sum is impossible.


Similarly, HCF plays a tiny but significant role in financial mathematics. It is true that it is not employed in advanced mathematics, but it is impossible to determine the link between distinct portions.

Elementary Mathematics

In this sense, HCF and LCM are fundamental terms from elementary mathematics. To avoid errors in your calculations, you should use several calculators available on the internet.

Final Thoughts

Both of these concepts are fundamental terms for all math students. Even basic-level problems are impossible to solve without these concepts.

You should learn how to solve the problems involving GCF and LCM by using all of the valid approaches. Calculators can help you learn from someone if you find it difficult to learn from them.

These tools will display a full answer including every step of the calculation, allowing you to comprehend every aspect of it. In brief, it will be the most effective technique to learn how to calculate the Least Common Multiple and Highest Common Factor.

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