LCM Calculator

How to Calculate the Least Common Multiple (LCM)

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the integers.

Formula

For two numbers a and b, the LCM can be calculated using the following formula:

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

Where:

• LCM is the Least Common Multiple
• GCD is the Greatest Common Divisor
• |a × b| is the absolute value of a multiplied by b

Calculation Steps

1. Find the GCD of the given numbers using the Euclidean algorithm.
2. Multiply the given numbers.
3. Divide the product by the GCD.
4. The result is the LCM.

Example

Let's find the LCM of 12 and 18:

1. First, calculate GCD(12, 18):
   • 18 = 12 × 1 + 6
   • 12 = 6 × 2 + 0
   • GCD(12, 18) = 6
2. Now apply the LCM formula: \[ LCM(12,18) = \frac{|12 \times 18|}{GCD(12,18)} = \frac{216}{6} = 36 \]

Therefore, the LCM of 12 and 18 is 36.

Visual Representation

This diagram illustrates how 36 is the smallest number that is divisible by both 12 and 18.