least

Least is the superlative form of the adjective little in English, used to denote the smallest in size, amount, degree, or extent. It functions as an adjective or determiner and can describe the minimum level required or identify the smallest item in a group, as in “the least effort” or “the least of these.”

In mathematics, least appears in several technical concepts. The least element of a partially ordered set is an element that is less than or equal to every other element. Not all posets have a least element; its existence is guaranteed in well-ordered or finite sets. When a set has a smallest element, that element is often called the minimum, though in general posets the term least is the precise descriptor. The least upper bound (supremum) is the smallest value that is greater than or equal to every element, while the greatest lower bound (infimum) is the largest value that is less than or equal to every element.

Common mathematical phrases using least include the least common multiple, the smallest number that is a multiple of each member of a given set of integers, and the method of least squares, a procedure for minimizing the sum of squared residuals in data fitting.

Beyond mathematics, least appears in everyday and formal use to indicate minimal thresholds or conditions, such as “the least amount of energy required.” The term derives from the English word little, with its comparative and superlative forms used to express increasing smallness.