Least Common Multiple (LCM) Calculator
Calculation
LCM(a, b) = |a * b| / GCD(a, b)
Understanding LCM
The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the integers without leaving a remainder. For example, the LCM of 4 and 6 is 12, because 12 is the smallest positive number that is divisible by both 4 and 6.
Like the GCD, the concept of the LCM is rooted in ancient number theory. Finding the LCM is closely related to finding the GCD. A fundamental relationship states that for two positive integers 'a' and 'b', their product equals the product of their LCM and GCD: a × b = LCM(a, b) × GCD(a, b). This relationship provides an efficient way to calculate the LCM once the GCD is known (using the Euclidean algorithm).
The LCM is commonly used when working with fractions, specifically for finding the least common denominator (LCD) needed to add or subtract fractions with different denominators. It also appears in solving problems involving cycles or periodic events that need to align, such as scheduling problems or wave interference patterns in physics.