Find the least common multiple (LCM) of two numbers
The LCM is calculated using the relationship LCM(a, b) = |a × b| / GCD(a, b). First, the Greatest Common Divisor (GCD) is found using the Euclidean algorithm, then the product of both numbers is divided by the GCD to yield the Least Common Multiple.
The LCM is essential for scheduling and synchronization problems, such as finding when two recurring events will coincide. It is also crucial in mathematics for adding or subtracting fractions that have different denominators by finding a common denominator.
The result is the smallest positive integer that is evenly divisible by both input numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6. The calculator also shows the GCD used in the computation.
When adding fractions with different denominators, use the LCM as your least common denominator for the simplest result. Remember that the LCM of any number and zero is zero, and the LCM of any number and one is that number itself.
The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is evenly divisible by all of those numbers. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number that both 4 and 6 divide into without a remainder.
The most efficient method uses the GCD: LCM(a, b) = |a x b| / GCD(a, b). First find the GCD using the Euclidean algorithm, then divide the product of the two numbers by the GCD. You can also list multiples of each number and find the smallest one they share, though this is slower for large numbers.
LCM is used whenever you need to synchronize repeating events. For example, if one bus arrives every 12 minutes and another every 15 minutes, the LCM (60 minutes) tells you when both will arrive at the same time. It is also essential for adding fractions with different denominators and for scheduling, gear ratios, and tiling problems.