## What is the Least Common Multiple (LCM)?

In mathematics, the least common multiple, also known as the lowest common multiple of two (or more) integers, is the smallest natural number divisible by all given numbers.

In most situations, it appears as LCM(n1, n2, ... n).

Example: LCM(8, 6, 2) = 24

## What is the full form of LCM?

LCM stands for Least Common Multiple also referred to as Lowest common multiple (LCM) or Least common Divisor (LCD).

## Why is it called LCM?

A common multiple is a number that can be found in any list of all given numbers.

A least common multiple (LCM) or least common divisor (LCD) is the smallest divisible number by all specified numbers.

## Characteristics of LCM

### LCM is associative

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

### LCM is commutative

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

### LCM is distributive

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

### LCM is related to the greatest common factor (GCF)

LCM(a,b) = a × b / GCF(a,b) and GCF(a,b) = a × b / LCM(a,b)

## Applications of Least Common Multiple (LCM)

LCM is used in engineering, astronomy, game theory, etc.

In engineering, for example, you may need to use a gear to move a torque downward or upward, so the radius and number of teeth required for a second meshing gear can be estimated using LCM.

In the same way, if you need to find out when the orbits of a planet or other cosmic bodies lead to a coincidence, as in the case of a solar or lunar eclipse, for example, when viewed from Earth, you can use: LCM.

Professionals in this field can use our lcm calculator, the best way to solve LCM problems quickly and easily.

## Why is this LCM calculator the best for finding the least common multiple?

This calculator calculates the LCM of two or more numbers using 5 different methods.

For each method, the calculator shows detailed step-by-step instructions.

Thanks to the Progressive Web App (PWA) feature, you can install it as an app on any device.

At the same time, it can handle LCM calculations for many numbers and calculate integers with up to 10 digits.

You can also enter numbers as desired, separated by commas.

## What are the different ways to find the LCM of two or more numbers?

Here are the five most common methods students and teachers use to determine the number of LCMs.

As follows:

Prime factorization Method

Listing Multiples Method

Division Method

Cake or ladder Method

Greatest Common Factor (GCF) Method

Note, it doesn't matter which LCM is computed first, as long as you use all the numbers when solving the LCM and follow the method exactly.

Each method has pros and cons depending on the specific situation, and you can decide which method to use at your discretion.

### How to Find LCM of a set of numbers using the Prime factorization Method?

Prime factorization involves breaking down each of the numbers being compared into its product of prime numbers.

The LCM is then determined by multiplying the highest power of each prime number together.

Note that computing the LCM this way, while more efficient than using the "brute force" method, is still limited to smaller numbers

Refer to the example below for clarification on how to use prime factorization to determine the LCM:

E.g: Find LCM(33, 56, 90) 33 = 3 x 11

56 = 2 x 2 x 2 x 7

90 = 2 x 3 x 3 x 5

The LCM is, therefore: = 8 x 9 x 11 x 7 x 5

LCM = 27720

### How to Find LCM of a set of numbers using the Listing Multiples Method

Listing multiples can be regarded as the simplest way to find the LCM of numbers.

In this method, you have to list down all the multiple of the numbers and then find the common multiple between these numbers which would be the LCM.

Take an example of finding the LCM of 8 and 14 using lists of multiple methods.

Firstly, write down the multiples of the given numbers.

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72

Multiples of 14 = 14, 28, 42, 56, 70, 84

Next, look out for the common multiple in the multiples of all numbers.

As we can see that the common number between the multiples of 8 and 14 is 56, which is the least common factor for these numbers.

LCM of 8 and 14 = 56

### How to Find LCM of a set of numbers using the Division Method

The division method is another method to get the LCM of multiple numbers.

First, we place all numbers on a horizontal line. Next, we start dividing the numbers beginning with the smallest prime number.

You write the quotient of division exactly below the dividend. Keep dividing until all numbers are fully divided and the remainder is 1.

### How to Find LCM of a set of numbers using the Cake or ladder Method

The cake and Ladder Method is the easiest and quickest method to find the LCM of a set of numbers. So people use most of this method because it is a simple division.

For instance, to find the LCM(10, 12, 15, 75):

You first write down your numbers in a cake layer (row). Next, divide the layer numbers by a prime number that is evenly divisible into two or more numbers in the layer, and bring down the result into the next layer.

If any number in the layer is not evenly divisible, bring down that number. Continue dividing cake layers by prime numbers.

When there are no more primes that are evenly divided into two or more numbers you are done.

### How to Find LCM of a set of numbers using the Greatest Common Factor (GCF) Method

This method is also called the LCM formula method.

The formula to find the LCM using the Greatest Common Factor GCF of a set of numbers is:

A factor is a number that results when you can evenly divide one number by another. In this sense, a factor is also known as a divisor.

The greatest common factor of two or more numbers is the largest number shared by all the factors.

LCM(a,b) = (a×b)/GCF(a,b)

Example: Find LCM(6,10)

Find the GCF(6,10) = 2

Use the LCM by GCF formula to calculate (6×10)/2

= 60/2

= 30

So LCM(6,10) = 30

## Cite this content, page, or calculator as:

Imoh, Nsikak, "Best LCM (Least Common Multiple) Calculator", [online] Available at: https://sikawebtools.com/lcm-calculator from sikawebtools, https://sikawebtools.com - Free tools