Least Common Multiple (LCM) Calculator
LCM Calculator
The Least Common Multiple (LCM) is the smallest number that both input numbers divide into evenly. It is essential for working with fractions and periodic events.
Conversion Formula
LCM(a, b) = |a × b| / GCD(a, b). We first find the GCD using the Euclidean algorithm, then divide the product by the GCD.
Step-by-Step Examples
12, 18 = LCM = 36
GCD(12,18) = 6, so LCM = 12×18/6 = 36.
4, 6 = LCM = 12
GCD(4,6) = 2, so LCM = 4×6/2 = 12.
Frequently Asked Questions
What is the LCM?
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by both numbers.
How is LCM related to GCD?
LCM(a, b) = |a × b| / GCD(a, b). Knowing the GCD makes finding the LCM efficient.
What is the LCM of two prime numbers?
The LCM of two different primes is their product. For example, LCM(3, 7) = 21.
When do you use LCM?
LCM is used to find common denominators for fractions, schedule recurring events, and solve problems involving cycles.
Can the LCM be less than either number?
No. The LCM is always at least as large as the larger of the two numbers.