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.

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