Define the least common multiple (LCM).

The least common multiple (LCM) is defined as the smallest multiple that two or more numbers share. This means that the LCM is the lowest positive integer that can be divided evenly by each of the numbers in a given set. For example, if you're finding the LCM of 4 and 5, you would look for the smallest number that both 4 and 5 can divide into without leaving a remainder, which is 20.

Understanding the LCM is crucial in various mathematical applications, such as finding common denominators in fractions or solving problems involving multiples. The emphasis is on finding the minimum value that meets the criteria of being a multiple of the given numbers, which distinguishes it from other concepts like the greatest common divisor (GCD).

While the other options refer to different mathematical concepts—like the largest shared multiple, the difference between numbers, or their sum—none of them accurately describe the definition of the least common multiple, which is centered around identifying the smallest shared multiple.