lcm
Học thuậtThân thiện
Definition
Noun The smallest positive integer that is a multiple of each number in a given set of integers. It is the smallest number into which all numbers of the set can divide without leaving a remainder.
Usage
The term lcm is used in mathematics, specifically in arithmetic and number theory, to find a common denominator for fractions or to solve problems involving synchronized events. It is typically used with the preposition "of" to specify the set of numbers.
Examples
- To add the fractions 1/4 and 1/6, you must first find the lcm of the denominators 4 and 6, which is 12.
- The lcm of 8 and 12 is 24.
- Calculate the lcm of 5, 6, and 15.
Advanced Usage
- In Algorithms: The concept of the lcm is fundamental in computer science algorithms, especially those dealing with periodic events or finding common cycles.
- Relationship with GCD: The lcm of two numbers, and , can be efficiently found using their greatest common divisor (gcd): lcm(a, b) = |a * b| / gcd(a, b).
Variants and Related Words
- Least Common Multiple (LCM): This is the full, unabbreviated form of lcm. The two terms are used interchangeably.
- The least common multiple is a fundamental concept in elementary number theory.
Synonyms
- Lowest Common Multiple: Primarily used in British English, identical in meaning to least common multiple.
Notes on Different Meanings
lcm is a highly specialized mathematical term with only one core meaning related to number divisibility. It does not have other common definitions, idioms, or phrasal verbs.
Noun
- the smallest multiple that is exactly divisible by every member of a set of numbers
- the least common multiple of 12 and 18 is 36