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lcm Calculator

LCM Calculator (Least Common Multiple)

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An online lcm calculator helps to find the least common multiple (lcm) of the two to ten or more numbers step-by-step by using different LCM calculation methods. This online least common multiple calculator allows you to estimate the lowest quantity that is the multiple of two or more numbers. Keep reading to know about how to find the least common multiple with different methods step-by-step, formulas for every method, and many other lcm related terms.

Now, let’s start with the basic definition of LCM.
Read on!

What is the least common multiple (LCM)?

The Least Common Multiple also known as Lowest Common Multiple is a basic mathematical function that determines the smallest integer that is divisible by each one of the integers. It is helpful before performing addition and subtraction of fractions with different denominators, to convert all fractions so that denominator is the least common multiple. In this case, lcm is also referred to as the Least Common Denominator (LCD).

So, simply consider our least common factor calculator that helps you to find the least common multiple step-by-step for your mathematical problem.

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?

Here are the five different LCM calculation methods discussed and manual calculation for each method. This lcm finder uses the following formulas for each method to find lcm of the given data set.

By Listing Multiples (Brute-Force Method):

The least common multiple (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 multiple 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.

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 least common multiple calculate 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.The procedure to find the least common multiple with GCF method is 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 to determine 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

By Division Method:

The division method is the last method that is used by our lcm calculator to find the lowest common multiple. This lowest common multiple calculator allows you to find the lcm of any set of numbers by the long division of numbers with its prime factors. We have an example to clear the concept.

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)?

Different properties of least common multiple is discussed below,

Least Common Multiple (LCM) is Commutative:

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

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

Least Common Multiple (LCM) 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 (LCM) is Distributive:

The lowest common multiple of numbers is distributive,

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

Where d is any constant.

About Least Common Multiple Calculator:

A simple lcm calculator will enable you to find the lowest common factor (lcm) or least common denominator (lcd) of two or n numbers. This lcm finder helps to calculate lcm (least common multiple) step-by-step corresponding to the following methods:

  • None (Simple Method for simplifying lcm)
  • Listing multiples method.
  • Prime factorization method.
  • GCF method.
  • Cake/ladder method.
  • Division method

How to find the Least Common Multiple by Least Common Multiple finder:

Finding the least common multiple of numbers becomes easy with this least common factor calculator. All you need to follow the given steps for finding lcm.

Read on!

Inputs:

  • First of all, you have to enter the numbers for which you want to calculate the least common multiple(LCM).
  • Then, select the lcm calculation method from the dropdown of this lowest common multiple calculator. It can either be “None(Simple)”, “Listing multiples”, ”Prime factorization”, ”GCF”, ”Cake/ladder” or “By division method”.
  • Finally, hit the “calculate” button.

Outputs:

Once you fill up all the field of this least common finder calculator, this will show you,

  • The least common multiple (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 very difficult to know the answer, then the least common multiple is an effective measure to determine the answer.

So, this lcm calculator shows step-by-step calculation of your real life 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.

End-Note (LCM):

The least common multiple is very helpful in the real world problems as well as in mathematics, especially for adding, subtracting, and comparing fractions. The LCM of the numbers helps in finding a quick solution and saves the time of students during the examination. Also, an online lcm calculator will perform lcm calculations for larger or larger sets of numbers accurately.

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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