Least Common Multiple Calculator

LCM Calculation:

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

Least Common Multiple (LCM):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Least Common Multiple?

The Least Common Multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers. It's a fundamental concept in number theory with applications in fractions, scheduling, and cryptography.

2. How Does the Calculator Work?

The calculator uses the relationship between LCM and GCD:

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

Where:

\( a \) — First integer
\( b \) — Second integer
GCD — Greatest Common Divisor

Explanation: The LCM is calculated by first finding the GCD using the Euclidean algorithm, then applying the formula above.

3. Importance of LCM Calculation

Details: LCM is essential for adding and subtracting fractions with different denominators, finding common time intervals in scheduling, and solving Diophantine equations in number theory.

4. Using the Calculator

Tips: Enter two positive integers. The calculator will compute their LCM. Both numbers must be positive integers (≥1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between LCM and GCD?
A: LCM finds the smallest shared multiple, while GCD finds the largest shared divisor of two numbers.

Q2: Can LCM be calculated for more than two numbers?
A: Yes, by iteratively applying LCM(a,b,c) = LCM(LCM(a,b),c).

Q3: What's the LCM of prime numbers?
A: The LCM of two distinct primes is their product. For the same prime, it's the number itself.

Q4: Is LCM defined for negative numbers?
A: Mathematically yes, but this calculator uses absolute values since LCM is always positive.

Q5: What's the relationship between LCM and GCD?
A: For any two numbers, LCM(a,b) × GCD(a,b) = |a×b| (as shown in the formula).