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lcm Calculator

LCM Calculator (Least Common Multiple)

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An online lcm calculator allows you to find the least common multiple (lcm) of a set of two, three, or more numbers. Moreover, this least common multiple calculator helps to find the lcm step-by-step by using 5 different methods:

  • None (Simple Method For Simplifying LCM)
  • Listing Multiples Method
  • Prime Factorization Method
  • GCF Method
  • Cake/Ladder Method
  • Division Method

With this informative content, you come to know how to find lcm (manually), formulas related to different lcm methods. But, first, we are going to share a basic overview of LCM.

Read on!

What is The Least Common Multiple (LCM)?

In mathematics, the LCM of two integers a and b is referred to as the smallest positive integer that is divisible by both a as well as b. For example, the lcm of 2, 5, and 7 is 70 as 70 is a multiple of 2, 3, and 7. However, there is no other number lower than 70, which is multiple of these three numbers. Well, LCM or Least Common Multiple is also named as:

  • Lowest Common Multiple
  • Smallest Common Multiple
  • Least Common Divisor (LCD)
  • Lowest Common Denominator
  • Least Common Factor

So, using an online lcm calculator is helps you to estimate the smallest number that is the multiple of two or n numbers.

Also, calculator-online provided the best fraction calculator that helps in adding, subtracting, multiplying, and dividing 2 or 3 fractions.

How to find LCM With Different Methods Step-by-Step?

We here going to tells you different methods of finding lcm and the given formulas for each individual method is used by our lcm finder to find lcm of the numbers.

By Listing Multiples (Brute-Force Method):

The LCM can be calculated by listing all the multiples of the given integers until the matched integer is reached. This method is also known as the Brute-Force method.

Here we have an example to clear the concept of calculation by listing the multiples.

For example:

What is the least common factor of 8,12 and 16?

Solution:

Multiples of 8 = 8,16,24,32,40,48,56,64

Multiples of 12 = 12,24,36,48,60,72

Multiples of 16 = 16,32,48,64,80

Here, the smallest number which is on all the lists is 48.

So, the LCM of 8,12,16 is 48.

No doubt, a manual calculation is a little much complicated, simply add the numbers into the least common multiple calculator and lets it do the remaining.

By Prime Factorization Method:

Another method to find the lcm of the given data set is the prime factorization method. Prime factorization includes the splitting of each number which is compared to the product of prime numbers. Then, the LCM calculated by multiplying the highest power of every prime with one another. This method is more efficient than the Brute-Force method. You can also use this free prime factorization calculator to make the prime factors of any number. Let’s try an example of this method:

For example:

Find out the lcm of 10,15 and 20?

Solution:

Prime factors of 10: 2 × 5

Prime factors of 15: 3 × 5

Prime factors of 20: 2 × 2 × 5

Then,LCM is = 5 × 2 × 2 × 3

= 60

By The Greatest Common Factor (GCF) Method:

The third feasible method to calculate the lcm of the integers is by greatest common factor method.It is also known as the greatest common divisor method. In GCF method, all you need to divide the product of numbers by their greatest common factor. The formula to find lcm with this method is as follow:

LCM (a,b) = a * b / GCF

For example:

Find the LCM of 4 and 10?

Solution:

The GCF of 4 and 10 = 2

LCM (4 ,10) = 4 * 10 / 2

LCM (4 ,10) = 20

By Cake/Ladder method:

The cake method finds the lcm of the given numbers with help of simple division. People use the cake/ladder method to find the least common multiple because it is the easiest way of finding lcm. Let’s try an example for this method.

For example:

Find the lcm of 8,12,14,20?

Solution:

Write the numbers in a row.

8,12,14,20

Divide the numbers by a prime number which is divisible by two or more numbers.

                                                                  2 8,12,14,20
                                                                  2 4,6,7,10
                                                                  2 2,3,7,5
                                                                  3 1,3,7,5
1,1,7,5

 

The lcm of 8,12,14,20 = 2 × 2 × 2 × 3 × 7 × 5

= 840

Finding lcm by using cake/ladder method looks like a daunting calculation, use an online lcm calculator that quickly calculates the least common divisor by using the cake method.

By Division Method: 

You can easily find the lcm of any set of numbers by using this method, you can look at the example to clear the concept. No doubt, long division is time taking method for finding lcm manually, our lowest common multiple calculator is a great way for determining least common factor instantly.

For example:

Find out the lcm of 6,12,15?

Solution:

Write the numbers in a row.

8,12,14,20

Divide the numbers by a prime number which is divisible by two or more numbers. Divide until the last term will be all one’s.

                                                                  2 8,12,14,20
                                                                  2 4,6,7,10
                                                                  2 2,3,7,5
                                                                  3 1,3,7,5
                                                                  5 1,1,7,5
                                                                  7 1,1,7,1
1,1,1,1

 

So,

The LCM of 8,12,14,20 = 2 × 2 × 2 × 3 × 5 × 7

= 120

What Are The Properties of Least Common Multiple (LCM)?

Let’s take a look at the given properties:

Least Common Multiple is Commutative:

The lcm of the two numbers is commutative,i;e

LCM (a,b) = LCM (b,a)

Least Common Multiple is Associative:

The lowest common multiple of three numbers is associative,

LCM (a,b,c) = LCM (LCM (a,b),c) = LCM(a,LCM(b,c))

Least Common Multiple is Distributive:

The lowest common multiple of numbers is distributive,

LCM (da,db,dc) = dLCM (a,b,c)

Where d is any constant.

How Least Common Multiple Calculator Works?

The least common factor calculator helps you to find the least common denominator of numbers within few steps, let’s take a look:

Read on!

Inputs:

  • First of all, you have to enter the numbers for which you want to calculate the LCM.
  • Then, select the lcm calculation method from the dropdown of this lcm calculator.

Outputs:

The least common finder calculator will calculate:

  • The LCM of the numbers according to the selected method.
  • Complete step-by-step calculations for the selected method.

Real-life Problem of LCM:

In a stationary, blue pencils come in a package of 16 while red pencils come in the package of 19. If we want to purchase equal numbers of both pencils, then find the smallest number of blue pencils that we must buy.

In this real-world problem, it is challenging to know the answer, so finding the least common denominator is an effective measure to determine the answer.

So, this lcm calculator shows the step-by-step calculation of your lowest common multiple math problems.

Frequently Ask Questions (FAQ’s):

What is the LCM of 12 15 and 21?

The least common multiple of 12,15 and 21 is 420.

What is the LCM of 4 and 8?

8 is the least common multiple of 4 and 8. This lcm calculator helps you to calculate the lcm of numbers according to different methods.

What’s the LCM of 24 and 36?

The least common multiple (LCM) of 24 and 36 is the smallest number which is exactly divisible by 24 and 36.72 is the smallest number which divides the 24 and 36 and gives zero remainders.

What is the LCM for 24 and 300 by prime factorization method?

For finding the least common multiple by prime factorization method, we have to write the factors of both numbers,

Prime factors of 24 = 2 × 2 × 2 × 3

Prime factors of 300 = 2 × 2 × 3 × 5 × 5

LCM = 2 × 2 × 3 × 2 × 5 × 5

LCM = 600

What is the LCM of 15 and 20?

This least common multiple calculator determines the lcm of 15 and 24 the smallest number is 60 which exactly divides the 15 and 24. So, the LCM of 14 and 24 is 60.

What is an example of LCM?

The multiple is a number that you get when multiplying a number with the whole number. Example: the multiples of 9 are 9,18,27,36,45,54,63,72,81,…

What is the LCM of 10 15 and 20?

The least common multiple (LCM) of 10,15 and 20 is 60 which is determined by multiplying the common & uncommon prime factors.

Wrapping it-up:

The least common multiple (divisor) of two or more numbers help you to determine quick solutions and highly best for K-12 educations. The concept of LCM in these days is play a key-role in solving problems related to racetracks, traffics lights, etc. Thanks to this free online lcm calculator through which you can readily find the lowest common multiple for two or n numbers.

References:

From the source of Wikipedia: Least common multiple (LCM), application, calculations, and much more

From the source of smartickmethod: How to Calculate Least Common Multiple: Category: Divisibility, Learning Resources

From the source of khanacademy: Legitimate information about Least common multiple (LCM) (CCSS.Math: 6.NS.B.4)

 

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