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What is GCF, and how is it different from LCM?
  • Sep 2021
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What is GCF, and how is it different from LCM?

4th September 2021

Are you confused about both of the terms? We are here to sort out your concepts.

GCF and LCM are both essential terms of mathematics, but these terms are different from each other.

Some people may mix up the concept, but they’ll never forget about GCF and LCM once they read this guide.

What is the term GCF?

GCF stands for the most significant common factor, and it refers to the largest positive integer that can be divided by each number.

The concept of GCF is totally in contrast to LCM because LCM is the lowest common multiple, and GCF is the most significant common factor.

GCF is one of the significant mathematical terms needed in necessary fields, either related to mathematics or physics.

We can find the greatest common factor by using a GCF calculator or finding it manually.

Why do we need GCF?

GCF is needed to simplify the fractions, and once you find out the most significant common factor, you can solve the equation.

It is also essential in some real-life problems, and most importantly, it is commonly used in algebra.

What is Least common multiple (LCM)?

It is pretty clear by the name that LCM is the smallest multiple that must be positive and common to two or more numbers.

We can say that LCM is the smallest integer that can be divisible by all the given numbers.

There are different methods of finding LCM in which multiple of a number and division method is included so you can use any of them.

How can we find LCM?

There are two methods of finding LCM; one is to calculate it manually, and the second is to use automated online tools.

We have many tools that can be the best LCM finder, and these tools are free of cost.

But it would help if you were known about the concept of LCM when you are going to solve this on your own. But, then, using tools is very easy.

Why do we need GCF and LCM?

When we are willing to deal with fractions, we need to use the most significant common factor and least common multiple.

But not only for fractions, but we also need these two expressions in different fields like LCM used in traffic lights problems.

And as it is mentioned above, GCF is commonly used in solving or simplifying fractions, so it is pretty apparent that GCF is important.

Methods of finding an LCM

There is more than one method to find out LCM, and each way is dependent on some factors, as some methods are suitable for extended expressions.

And some of the methods are good for shorter and less complex expressions, but each is used to find put LCM.

Let’s have a look.

  1. Listing multiples

Listing multiples is a fundamental and common method of finding an LCM, and it is widely used to solve significant expressions.

This method is quite simple, and you don’t need those skills to solve your question by this method.

Here we have an example. 

If we want to find out the LCM of 10 and 25, we need to list the multiples of both numbers.

The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.

Then it comes to the multiples of 25, and we have 25, 50, 75, and 100. As we see, 100 comes in both of the lists so, 100 is considered as LCM.

  1. Prime factors method

The second method of finding an LCM is to use the prime factors of a given number. Again, we can explain this by a simple example.

If you want to take an LCM of 12 and 18 so, you need to display the prime factors of both of the numbers.

Prime factors of 12 are 2.2.3, and prime factors of 18 are: 2.3.3

We must take a product of these factors, and the output will be the LCM.

Bottom line

Mathematics can be a hectic job for many people, but it can be easy for you if you are using tools to sort out mathematical problems.

Hundreds of mathematical terms need to solve very efficiently, and you must use a calculator for those terms.

We have discussed the concept of GCF and LCM so, and it is not confusing anymore.



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