Elementary arithmetic is the simplified portion of arithmetic which includes the operations of addition, subtraction, multiplication, and division.
Elementary arithmetic starts with the natural numbers and the written symbols (digits) which represent them. The process for combining a pair of these numbers with the four basic operations traditionally relies on memorized results for small values of numbers, including the contents of a multiplication table to assist with multiplication and division.
In arithmetic and number theory, the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a,0) for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.
The LCM is familiar from grade-school arithmetic as the "least common denominator" (LCD) that must be determined before fractions can be added, subtracted or compared.
In computing, the X Window System (X11, X, and sometimes informally X-Windows) is a windowing system for bitmap displays, common on UNIX-like operating systems.
X provides the basic framework for a GUI environment: drawing and moving windows on the display device and interacting with a mouse and keyboard. X does not mandate the user interface — this is handled by individual programs. As such, the visual styling of X-based environments varies greatly; different programs may present radically different interfaces.
Multi-speed Europe or two-speed Europe (called also variable geometry Europe or Core Europe depending on the form it would take in practice) is the idea that different parts of the European Union should integrate at different levels and pace depending on the political situation in each individual country. Indeed, multi-speed Europe is currently a reality, with only a subset of EU countries members of the eurozone and of the Schengen area. Like other forms of differentiated integration such as à la carte and variable geometry, multi-speed Europe arguably aims to provide a solution to the dilemma between unity and diversity, widening and deepening of the European Union.