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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.

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

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.

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

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

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`

.

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

Example 1:

Find the LCM of 6 and 8.

Solution:

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

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

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

Therefore, the LCM of 6 and 8 is 24.

Example 2:

Find the LCM of 15 and 25.

Solution:

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

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

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

Therefore, the LCM of 15 and 25 is 75.

Example 3:

Find the LCM of 2 and 9.

Solution:

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

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

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

Therefore, the LCM of 2 and 9 is 18.

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