lowest common multiple

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lowest common multiple

The teacher writes the lowest common multiple of 12 and 18 on the chalkboard.

Definition
  1. Noun:
    • The smallest positive integer that is a multiple of each number in a given set: The "lowest common multiple" (LCM) is the smallest number that can be divided evenly by every number in a specified set of integers. It is a fundamental concept in arithmetic and number theory.
Usage and Examples
  • Noun:
    • To add fractions with different denominators, you must first find the lowest common multiple of the denominators.
    • The lowest common multiple of 4, 5, and 10 is 20.
    • Calculating the lowest common multiple is essential for solving problems involving synchronized events, like when two bells ring at different intervals.
Advanced Usage
  • "Find the lowest common multiple of...": A standard instructional phrase used in mathematics.
    • The first step in the problem is to find the lowest common multiple of 6 and 15.
  • Used in algebraic contexts for polynomials.
    • The process for finding the lowest common multiple of algebraic expressions is similar to that for integers.
Variants and Related Words
  • Least Common Multiple (LCM): This is a full and perfectly synonymous variant of "lowest common multiple." The abbreviation "LCM" is very common.
    • The LCM of 8 and 12 is 24.
  • Common Multiple: A number that is a multiple of two or more numbers. The "lowest common multiple" is the smallest of all common multiples.
    • 60 is a common multiple of 12 and 15, but it is not the lowest one.
Synonyms
  • Least Common Multiple: The direct and most frequent synonym.
  • Smallest Common Multiple: A descriptive synonym that clarifies the meaning.
Antonyms / Contrasting Terms
  • Greatest Common Divisor (GCD): The largest positive integer that divides each of the numbers without a remainder. This is a complementary concept often studied alongside the LCM.
    • While the LCM of 12 and 18 is 36, their greatest common divisor is 6.
lowest common multiple

The teacher writes the lowest common multiple of 12 and 18 on the chalkboard.

Noun
  1. 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

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