Least Common Multiple Calculator

Understanding Least Common Multiple (LCM)

What is the Least Common Multiple?

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the integers. It's a fundamental concept in number theory and has various applications in mathematics and real-world problem-solving.

Formula for LCM

The LCM of two numbers a and b can be calculated using the following formula:

\[LCM(a,b) = \frac{|a \times b|}{GCD(a,b)}\]

Where:

• |a × b| is the absolute value of the product of a and b
• GCD(a,b) is the Greatest Common Divisor of a and b

Calculation Steps

Let's find the LCM of 12 and 18:

1. Calculate the GCD of 12 and 18 (which is 6)
2. Multiply 12 and 18: 12 × 18 = 216
3. Divide the product by the GCD: 216 ÷ 6 = 36

Therefore, LCM(12, 18) = 36

Example and Visual Representation

This diagram illustrates the relative sizes of 12, 18, and their LCM (36).