GCF and LCM Calculator which is short of greatest common factor and least common multiple calculator determine the greatest and least common factors of two or more numbers. As we all know, there are times when we need to adjust how a formula or integer appears to continue to calculate the problem.
Our tool is here to help you find what you may need. Please continue reading to find out how to use our calculator, and there is also an example for easier understanding.
Greatest Common Factor
The greatest common factor, or GCF, is the largest number factor between a set of integers. Furthermore, some also know it as the greatest common denominator or highest common divisor. We commonly apply it when dealing with polynomials for pulling common factors.
There are multiple ways of finding what the GCF of given numbers is, and they are:
- list of factors,
- prime factorization,
- Euclidean algorithm,
- Binary greatest common divisor algorithm, and
- Coprime numbers.
Least Common Multiple
The least common multiple is the lowest common multiple between two or more numbers. It is similar to the Highest Common Divisor, which we mentioned before, and they are closely connected.
The method used to find LCM is by taking each integer given and breaking them into their prime factors, which we will explain further below, together with GCF. In our calculator, the result of LCM will be shown right below GCF division.
On the other hand, there is also our Least Common Denominator – LCD Calculator as well, so make sure to check it out.
How to use the GCF Finder?
Here we will explain how to find GCF. Let’s say we have two numbers, 20 and 30. You will be able to find it by following the next steps:
- first task is to get the prime factorizations of given numbers: 20= 2\cdot2\cdot5 and: 30=2\cdot3\cdot5
- The greatest common factor between these two numbers is ten, and LCM is 60.
All this can be easily calculated in our GCF and LCM Calculator.
Example – How to find GCF and LCM?
There are many methods of finding both GCF and LCM, and here, we will explain some of them, first focusing on GCF, followed by methods of finding LCM.
List of factors
A list of factors is the primary method used in math to calculate the GCF, and that is to find all the factors of the given set of numbers.
For example, we will take two numbers, 25 and 40, and our task is to find all factors of these numbers. Factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40 and 25: 1, 5, 25.
The next step is to list all common factors: 1, 5, therefore GCF of 25 and 40 is 5, the greatest value of the listed above. Even though it may be easy to estimate and find GCF by this method on a small number, it gets exponentially harder with larger numbers, so we recommend using our tool for simpler and faster computations.
Prime factorization
Another method that we can often apply to find GCF is prime factorization, mostly due to its similarity with the previous one. The only difference is that instead of listing all factors, you only list prime numbers. For this example, we will take numbers 15 and 25.
15: 3,5
25: 5,5
In other words, we can write these numbers as 3\cdot5 and 5\cdot5 respectively.
The prime factors both of them share are five, which is the greatest common denominator here.
There are more different methods of finding GCF. Still, since we have our calculator here to do the job, we mentioned only the most common.
LCM Examples
Now, our next part is about methods of finding LCM. Even though GCF and LCM are similar and have similar methods, when dealing with finding the LCM, it is good to keep in mind several divisibility rules used in math, which can help and ease the process, such as:
- All even numbers are divisible by two.
- When summed, any number whose digits are equal to 3 is divisible by three.
- All numbers that end in 5 or 0 are divisible by five.
- Any number that ends in 0 is divisible by ten.
List of multiples
List of multiples is one of the methods we often use. It is simple as it sounds; all you need to do is list multiples of each number given and keep multiplying until you find the lowest one shared by all numbers. For example, let’s say we have numbers 2 and 3, and now, we will list their multiples:
2: 2, 4, 6, 8, 10...
\newline3: 3, 6, 9, 12, 15, 18...
6 is the LCM between these two numbers.
Prime factorization
While it is easy to list them when dealing with small numbers, it is taxing to do so with a much larger number that does not have LCM in their lower multiples. Because of that, we have this method, which is listing prime factors of given numbers, which can be done using a factor tree.
For this example, we will take numbers 42 and 38. Let’s start by listing the prime factors of each integer.
42: 2\cdot3\cdot7
38: 2\cdot19
The next step is to multiply all the factors we got, but keep in mind to only count the 2s once:
\newline2\cdot19\cdot3\cdot7=798
LCM of 38 and 42 is 798.
We can calculate all this in our GCF and LCM calculator and only needs an input of given integers, whether two or more.
Difference between GCF and LCM
Even though GCF and LCM are mentioned in the same article and have almost the same methods of finding them, they have their differences. The main difference between them is found in the meaning and definition of the two terms. Below is a table showing dissimilarities between them.
| Parameters of comparison | GCF | LCM |
| Definition | The largest number which divides a group of 2 or more numbers into two or more equal parts. | It is a number that shows the lowest common multiple of a set of integers. |
| Full-Form | Greatest Common Factor | Least Common Multiple |
| Meaning | All given integers share the largest number. | The smallest number can be later divided by the numbers given. |
| Type of Number | Prime numbers. | Composite numbers. |
| Synonyms or other terms used | Highest Common Factor, Greatest Common Denominator | Lowest Common Multiple |
That’s it; we hope our GCF and LCM calculator will help you do your math problems; also, check out other similar tools in the math section, such as Factorial Calculator, Area Calculator, Complex Conjugate, or do the division of radicals and get your result with this Dividing Radicals Calculator.
