Least Common Multiple

In mathematics, LCM (least common multiple) is a key concept that is used to find the smallest number that is a multiple of two or more than two numbers. This can be an important calculation to make when you are trying to solve problems. In this blog post, we will teach you how to calculate LCM using different methods. We will also show you examples of how LCM can be used in real-world situations.

Least Common Multiple

LCM is short for Least Common Multiple. LCM is the smallest number (not zero) that is a multiple of two or more than two numbers. LCM is used in many different ways, including finding the greatest common divisor (GCD).

The LCM (least common multiple) is a mathematical calculation that determines the smallest number that is divisible by two or more than two numbers.

Properties Of LCM

Some of the properties of LCM are:

• LCM of two numbers is always equal to or greater than their HCF (Highest Common Factor)
• LCM of more than three numbers can be found by finding the LCM of all pairs of numbers and then taking the LCM of those results
• LCM is associative (a*b)*c = a*(b*c)
• LCM is distributive (a+ b) * LCM (a,b)= LCM (a,b) * LCM (a+ b)
• Product of two numbers is always equal to the product of their HCF and LCM
• LCM of any number with zero is always equal to zero. LCM of a number with unity is always equal to the number itself. LCM (x,y) = LCM(x, LCM(y, x))

Difference between HCF and LCM

The LCM (Least Common Multiple) is the smallest number that is a multiple of two or more than two numbers. The HCF (Highest Common Factor) is the largest number that divides exactly into two or more than two numbers. LCM and HCF are also called GCD (Greatest Common Divisor).

How To Calculate LCM?

If you are looking for answers to “how to calculate LCM (Least Common Multiple)”, here are some ways to calculate the smallest number that is a multiple of two or more than two numbers. LCM can be calculated by:

-using prime factorization

-listing multiples

-ladder methods

-finding LCM with prime numbers

-using Venn Diagrams LCM helps to find the LCM of a set of integers.

-using division method

Prime Factorization

The first method is to use the prime factorization of two numbers. LCM can be found by multiplying all the prime factors of one number with the other number that are not present in LCM.

Steps to find LCM from Prime Factorization:

• Determine all of a number’s prime factors
• List all prime numbers found, in the order in which they appear most frequently for each given number
• To find the LCM, multiply the list of prime factors together

For example : What is the LCM of 13 and 12. Use prime factorization method:

LCM (13, 12)

12 = 2 x2x 3 is a prime factorization.

30 = 2x 3x 5 is a prime factorization.

Using all prime numbers identified in the order in which they occur most frequently, we get 2 x2x 3x 5 = 60.

As a result, LCM(12,30) = 60.

Listing Multiples

Steps:

• List each number’s multiples until at least one of them appears on all of the lists
• Determine the least number on all of the lists
• This is the LCM number

For example: What is the LCM of 12 and 18?

– Multiples of 12: 12, 24, 36, 48.

-Multiples of 18:  18, 36, 54, 72.

– LCM of 12 and 18 is 36.

Division Method

In a top table row, write down your numbers.

• Divide all the numbers in the row by a prime number. The prime number must be completely divisible into at least one of your numbers, starting with the lowest prime numbers, then carrying the result down into the next table row.
• If any of the numbers in the row are not equally divisible, reduce that number.
• Divide the rows by prime numbers that divide equally into at least one number and so on.
• You’re done when the last row of results is all 1’s.

The LCM is the product of the first column’s prime numbers.

Conclusion 

The LCM is a crucial component of understanding how to solve equations in mathematics.