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A least common multiple of a and b is a common multiple that is minimal, in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one. However, any two least common multiples of the same pair of elements are associates. [10]
In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.
Least common multiple, a function of two integers; Living Computer Museum; Life cycle management, management of software applications in virtual machines or in containers; Logical Computing Machine, another name for a Turing machine
For example, 1 is the infimum of the positive integers as a subset of integers. For another example, consider again the relation | on natural numbers. The least upper bound of two numbers is the smallest number that is divided by both of them, i.e. the least common multiple of the numbers.
Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π. Quadratic surd: A root of a quadratic equation with rational coefficients. Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number.
Least common denominator – Least common multiple of two or more fractions' denominators; Factoring – Breaking a number down into its products Fundamental theorem of arithmetic; Prime number – Number divisible by only 1 or itself Prime number theorem; Distribution of primes; Composite number – Number made of two smaller integers
m and n are coprime (also called relatively prime) if gcd(m, n) = 1 (meaning they have no common prime factor). lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and ...
Every pair of congruence relations for an unknown integer x, of the form x ≡ k (mod a) and x ≡ m (mod b), has a solution (Chinese remainder theorem); in fact the solutions are described by a single congruence relation modulo ab. The least common multiple of a and b is equal to their product ab, i.e. lcm(a, b) = ab. [4]