# GCF and LCM Calculator

GCF and LCM Calculator: If you ever need assistance with finding the Greatest Common Factor and Least Common Multiple of numbers take the help of the free tool. Apart from saving you ample time by giving the GCF and LCM easily this GCF and LCM Calculator provides you a detailed description explaining the concept. You can use the manual procedure explained to do GCF and LCM by hand and get a grip on various methods to find GCF and LCM.

## Online GCF and LCM Calculators List

Free Online GCF and LCM Tools provided over here will find the Greatest Common Factor and Least Common Multiple within split seconds. You can find the below-attached LCM and GCF related tools for finding LCM & GCF of two numbers, two or more numbers, etc. We have covered everthing at Onlinecalculator.guru related to Least Common Multiple & Greatest Common Factor.

### LCM Calculator

Ex: Find the LCM of 12 and 24

Check out the procedure to find the Least Common Multiple of 12 and 24 using the Prime Factorization Method. They are as follows

Step 1: Firstly, find the Prime Factorization of given numbers 12, 24

Prime Factorization of 12 is as such

 2 12 2 6 3 3 1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponent form is:

12 = 22×31

Prime Factorization of 24 is as follows

 2 24 2 12 2 6 3 3 1

Prime factors of 24 are 2,3. Prime factorization of 24 in exponent form is:

24 = 23×31

Step 2: Multiply together each of the Prime Numbers with the highest power to obtain the Least Common Multiple

On doing so, you will get the resultant equation as 23×31= 24

Therefore, LCM of two numbers 12 and 24 is 24

LCM(12,24) = 24

Here are some samples of LCM of two numbers calculations.

### GCF Calculator

Ex: Find the GCF of 16 and 24

Given Inputs are 16, 24

To find the GCF using the Prime Factorization Method you just need to list out the prime factors of both the numbers.

Prime Factorization of 16 as under

 2 16 2 8 2 4 2 2 1

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 24

Prime Factorization of 24 is as such

 2 24 2 12 2 6 3 3 1

Prime factors of 24 are 2.Prime factorization of 24 in exponential form is:

24 = 23×31

Occurrences of Common Prime Factors from both the numbers 16 and 24 is 8

Therefore, GCF of two numbers 16 and 24 is 8

### GCF of 16, 24 using Factoring Method

Given input data is 16, 24

Make a list of factors for the corresponding input numbers

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1,2,3,4,6,8,12,24

Figure out the highest common factor from factors of both the numbers and that is the GCF. In this case, it is 8

Therefore, GCF of two numbers 16 ad 24 is 8

Here are some samples of GCF of two numbers calculations.

### LCM of two or more Numbers Calculator

Ex: Find the LCM of 12, 24 and 36

Arrange the Inputs 12,24,36 in a horizontal line separated by commas and divide them with a prime number. Note the quotients in the next row and divide with quotients with prime numbers again. Continue the process until you have all co primes in the last.

 2 12, 24, 36 2 6, 12, 18 3 3, 6, 9 1, 2, 3

As all the numbers left in the last row are co primes you need not do the common division process further.

To obtain the Least Common Multiple, multiply the prime numbers with which you have divided the given numbers and the co primes in the last row i.e. 2 x 2 x 3 x 1 x 2 x 3 = 72

Therefore, LCM of 12,24,36 is 72

### Finding LCM of 12,24,36 using GCF Formula

Step1:

Let's calculate the LCM of first two numbers

The formula of LCM is LCM(a,b) = ( a x b) / GCF(a,b)

GCF(12, 24) = 12

LCM(12, 24) = ( 12 x 24 ) / 12

LCM(12, 24) = 288 / 12

LCM(12, 24) = 24

Step2:

Here we consider the LCM from the above i.e. 24 as first number and the next as 36

The formula of LCM is LCM(a,b) = ( a x b) / GCF(a,b)

GCF(24, 36) = 12

LCM(24, 36) = ( 24 x 36 ) / 12

LCM(24, 36) = 864 / 12

LCM(24, 36) = 72

LCM of 12,24,36 is 72

Here are some samples of LCM of two or more Numbers calculations.

### GCF of two or more Numbers Calculator

Ex: Find the GCF of 8, 20, 48

Given Input numbers are 8, 20, 48

To find the GCF of numbers using factoring list out all the factors of each number

Factors of 8

List of positive integer factors of 8 that divides 8 without a remainder.

1, 2, 4, 8

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Greatest Common Factor

We found the factors of 8, 20, 48 . The biggest common factor number is the GCF number.
So the Greatest Common Factor 8, 20, 48 is 4.

Therefore, GCF of numbers 8, 20, 48 is 4

### Finding GCF of 8, 20, 48 using Prime Factorization

Given Input Data is 8, 20, 48

Make a list of Prime Factors of all the given numbers initially

Prime Factorization of 8 is 2 x 2 x 2

Prime Factorization of 20 is 2 x 2 x 5

Prime Factorization of 48 is 2 x 2 x 2 x 2 x 3

Highest common occurrences in the given inputs are 22

Multiplying them we get the GCF as 4

Here are some samples of GCF of two or more Numbers calculations.

### Factoring Calculator

Ex: Find the Factors of 128

Positive integers that divides 128 without a remainder are listed below.

• 1
• 2
• 4
• 8
• 16
• 32
• 64
• 128

### Factors of 128 in pairs

• 1 × 128 = 128
• 2 × 64 = 128
• 4 × 32 = 128
• 8 × 16 = 128
• 16 × 8 = 128
• 32 × 4 = 128
• 64 × 2 = 128
• 128 × 1 = 128

### Factors of 128 Table

Factor Factor Number
1 one
2 two
4 four
8 eight
16 sixteen
32 thirty two
64 sixty four
128 one hundred twenty eight

Here are some samples of factoring calculations.

### Prime Factorisation Calculator

Ex: Find the Prime Factors of 256

One of the methods to check the Prime Factor of a number is trial division. Trial division consists of very easy and basic algorithms, though it is an extremely slow process. In this method, we have to check each number by dividing the composite number in question by the integer and deciding if, and how many times, the number can divide the number equally.

To get the prime factorisation of 256, we have to start with dividing it by primes

256 ÷ 128 = 2

128 ÷ 64 = 2

64 ÷ 32 = 2

32 ÷ 16 = 2

16 ÷ 8 = 2

8 ÷ 4 = 2

4 ÷ 2 = 2

2 ÷ 1 = 2

So here he prime factorisation of 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28

We can check it in a prime factorisation calculator also. The algorithm used in the calculator and trial division may differ but the result is always the same.

Here are some samples of Prime Factorisation calculations.

### HCF Using Euclid's division lemma Calculator

Ex: Find the HCF of 196 and 38220

Below detailed show work will make you learn how to find HCF of 196,38220 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(196,38220).

Here 38220 is greater than 196

Now, consider the largest number as 'a' from the given number ie., 38220 and 196 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 38220 > 196, we apply the division lemma to 38220 and 196, to get

38220 = 196 x 195 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 196, the HCF of 196 and 38220 is 196

Notice that 196 = HCF(38220,196) .

Therefore, HCF of 196,38220 using Euclid's division lemma is 196.

Here are some samples of HCF Using Euclids Division Algorithm calculations.

### Factor Tree Calculator

Ex: Find the Factor Tree of 512

Factor Tree of 512 is the list of prime factors when multiplied it results in the original number ie., 512.

Factor Tree is the easiest way to find the factors of a given number. So, draw the factor tree of 512 and express all its prime multiplies.

512 = 2 x 256

256 = 2 x 128

128 = 2 x 64

64 = 2 x 32

32 = 2 x 16

16 = 2 x 8

8 = 2 x 4

4 = 2 x 2

If we write into multiples it would be 512 x 2

On splitting 256 further and writing it as multiples of numbers it would be 128 x 2.

On splitting 128 further and writing it as multiples of numbers it would be 64 x 2.

On splitting 64 further and writing it as multiples of numbers it would be 32 x 2.

On splitting 32 further and writing it as multiples of numbers it would be 16 x 2.

On splitting 16 further and writing it as multiples of numbers it would be 8 x 2.

On splitting 8 further and writing it as multiples of numbers it would be 4 x 2.

On splitting 4 further and writing it as multiples of numbers it would be 2 x 2.

Altogether expressing the 99 in terms of prime factors would be 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2. And the factor tree of 512 would be like shown below: Here are some samples of Factor Tree calculations.

### LCM of Decimals Calculator

Ex: Find the LCM of 3.6 and 4.8

Given numbers are 3.6,4.8. The highest number of digits after the decimal point in the given case is 1

Thus, in order to get rid of the decimal point we need to multiply them with 10. On doing so, they are as follows

3.6 x 10 = 36

4.8 x 10 = 48

On finding the LCM of 36,48 we get the Least Common Multiple as 144

Arrange the Inputs 36,48 in a horizontal line separated by commas and divide them with a prime number. Note the quotients in the next row and divide with quotients with prime numbers again. Continue the process until you have all co primes in the last.

 2 36, 48 2 18, 24 3 9, 12 3, 4

As all the numbers left in the last row are co primes you need not do the common division process further.

To obtain the Least Common Multiple, multiply the prime numbers with which you have divided the given numbers and the co primes in the last row i.e. 2 x 2 x 3 x 3 x 4 = 144

Therefore, LCM of 36,48 is 144

Divide the result you got with the number you multiplied to make it as integer in the first step. In this case, we need to divide by 10 as we used it to make the given numbers into integers.

On dividing the LCM 144/10 we get 14.4

Thus the Least Common Multiple of 3.6,4.8 is 14.4

Here are some samples of LCM of Decimals calculations.

### GCF of Decimals Calculator

Ex: Find the GCF of 3.6 and 4.8

Given numbers are 3.6,4.8. The highest number of digits after the decimal point in the given case is 1

First, check the number of decimal points for both given decimals. That is equal to 1. So, multiply both of them with 10 and convert them into integers.

On doing, we see the integers as under

3.6 x 10 = 36

4.8 x 10 = 48

On finding the GCF of 36,48 we get the Greatest Common Factor as 12

 2 36, 48 2 18, 24 3 9, 12 3, 4

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Now, Divide the GCF i.e., 12 with the multiplied number before ie., 10 and make the integer result into decimal.

By dividing the GCF we get = 12/10 = 1.2

On doing, we will get the end result ie., GCF of 3.6,4.8 is 1.2

Here are some samples of GCF of Decimals calculations.

### GCF of Fractions Calculator

Ex: Find the GCF of Fractions 3/6 and 4/8

Step 1: Take the given fractions 3/6,4/8

Step 2: Apply the Formula for finding the Greatest common factor of 3/6,4/8 ie.,

GCF of Fraction = GCF of Numerators/LCM of Denominators

Step 3: Separate the numerators part and denominators part and find the GCF and LCM of fractions

Step 4: After getting the result we have put then in formula to get GCF.

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 3,4

Greatest Common Factor of Numerators i.e. GCF of 3,4 is 1 .

LCM of Denominators means LCM of 6,8 as per the given fractions.

LCM of 6,8 is 24 as it is the smallest common factor for both these numbers.

Therefore, LCM of 6,8 is 24

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/24

Therefore, the GCF of Fractions 3/6,4/8 is 1/24

Here are some samples of GCF of Fractions calculations.

### LCM of Fractions Calculator

Ex: Find the LCM of Fractions 1/2 and 3/5

Given Input Data is 1/2,3/5

As per the formula LCM of Fractions = LCM of Numerators/GCF of Denominators

LCM of Numerators means (1,3) in this case as per given inputs

Least Common Multiple of 1,3 is 3 the smallest number that is divisible by the numbers

GCF of Denominators means (2,5) in this case as per given inputs

Greatest Common Factor of 2,5 is 1 the largest number by which both the numbers can be divided

∴ So GCF of numbers is 1 because of no common factors present between them.

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 3/1

Therefore the LCM of Fractions 1/2,3/5 is 3

Here are some samples of GCF of Fractions calculations.

### FAQs on GCF and LCM

1. How do you find the GCF and LCM on a Calculator?

All you need to do is input the numbers in the input fields of the calculator and tap on the calculate button to get the result instantly.

2. What is meant by LCM?

LCM stands for Least Common Multiple and is the smallest positive integer that is evenly divisible by both the numbers.

3. What is the full form of GCF?

GCF stands for Greatest Common Factor. It is also known as Greatest Common Divisor(GCD) or Highest Common Factor(HCF).

4. What is it called when the GCF is 1?

When GCF is 1 the numbers are said to be relatively prime.