How is the least common multiple defined?

The least common multiple (LCM) is specifically defined as the smallest positive integer that all of the given numbers can divide into without leaving a remainder. This means that when you find the LCM of a set of numbers, you are looking for the least value that is a multiple of each number in the set.

For instance, if you were to find the LCM of 4 and 6, the multiples of 4 are 4, 8, 12, 16, and so forth, while the multiples of 6 are 6, 12, 18, and so on. The smallest multiple that appears in both lists is 12, making it the LCM. This understanding directly aligns with the correct definition that the answer provides.

Understanding that the LCM is focused on the smallest of these common multiples is crucial when solving problems involving multiples and divisibility, distinguishing it clearly from concepts like greatest common divisor or summation of numbers.