# LCM Calculator

The LCM Calculator is a powerful tool designed to assist you in understanding and calculating the least common multiple of numbers. LCM is a fundamental concept in mathematics, especially in arithmetic and number theory. It helps find the smallest number that is a multiple of two or more given numbers.

The LCM Calculator is a powerful tool designed to assist you in understanding and calculating the least common multiple of numbers. LCM is a fundamental concept in mathematics, especially in arithmetic and number theory. It helps find the smallest number that is a multiple of two or more given numbers.

### What is LCM?

LCM stands for Least Common Multiple . It is thesmallest positive integer that is a multiple of two or more given numbers.

### Why is LCM important?

LCM has various applications in mathematics, including:

• Adding and subtracting fractions with different denominators.
• Solving equations with common denominators.
• Finding the least common period in repeating decimals.

### How to calculate LCM?

There are different methods to calculate LCM, but the calculator uses the following formula:

`$\text{LCM}\left(a,b\right)=\frac{|a×b|}{\text{GCD}\left(a,b\right)}$`

where:

• `a` and `b` are the numbers.
• `|a * b|` represents the absolute value of the product of `a` and `b`.
• `GCD(a, b)` represents the Greatest Common Divisor of `a` and `b`.

### How does the LCM Calculator work?

Simply enter the numbers you want to find the LCM of, and the calculator will instantly compute and display the result.

### Examples

Example 1:

Find the LCM of 6 and 8.

Solution:

`$\text{LCM}\left(6,8\right)=\frac{|6×8|}{\text{GCD}\left(6,8\right)}$`

`$\text{LCM}\left(6,8\right)=\frac{|\mathrm{48}|}{2}$`

`$\text{LCM}\left(6,8\right)=\frac{\mathrm{24}}{}$`

Therefore, the LCM of 6 and 8 is 24.

Example 2:

Find the LCM of 15 and 25.

Solution:

`$\text{LCM}\left(\mathrm{12},8\right)=\frac{|\mathrm{15}×\mathrm{25}|}{\text{GCD}\left(\mathrm{15},\mathrm{25}\right)}$`

`$\text{LCM}\left(\mathrm{15},\mathrm{25}\right)=\frac{|\mathrm{375}|}{5}$`

`$\text{LCM}\left(\mathrm{15},\mathrm{25}\right)=\frac{\mathrm{75}}{}$`

Therefore, the LCM of 15 and 25 is 75.

Example 3:

Find the LCM of 2 and 9.

Solution:

`$\text{LCM}\left(2,9\right)=\frac{|2×9|}{\text{GCD}\left(2,9\right)}$`

`$\text{LCM}\left(2,9\right)=\frac{|\mathrm{18}|}{1}$`

`$\text{LCM}\left(2,9\right)=\frac{\mathrm{18}}{}$`

Therefore, the LCM of 2 and 9 is 18.