1. What is LCM?

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 LCM formula:

Where:

• \( a \) — First integer
• \( b \) — Second integer
• \( \gcd(a, b) \) — Greatest common divisor of a and b

Explanation: The formula calculates LCM by first finding the GCD using the Euclidean algorithm, then applying the relationship between GCD and LCM.

3. Importance of LCM Calculation

Details: LCM is essential for adding and subtracting fractions with different denominators, finding common event schedules, and solving problems in modular arithmetic.

4. Using the Calculator

Tips: Enter two positive integers. The calculator will compute their LCM using the GCD-based formula for optimal efficiency.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between LCM and GCD?
A: GCD is the largest number that divides both inputs, while LCM is the smallest number that both inputs divide into.

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

Q3: What is 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: How does LCM relate to fraction operations?
A: LCM of denominators serves as the least common denominator when adding/subtracting fractions.

Q5: What's the time complexity of this method?
A: O(log(min(a,b))) due to the Euclidean algorithm for GCD calculation.