common multiple

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common multiple

A student circles the common multiple on a math worksheet.

Definition
  1. Noun:
    • An integer that is a multiple of two or more other integers: A number that can be divided evenly by each of a given set of numbers. It is a shared multiple of those numbers.
Usage
  • The term "common multiple" is used in mathematics, specifically in arithmetic and number theory. It describes a number that is a product of two or more integers. When finding common multiples, one typically lists the multiples of each number and identifies the numbers that appear in all lists.
  • It is often used in the context of finding the least common multiple (LCM), which is the smallest positive common multiple of a set of numbers.
Examples
  • Noun:
    • The numbers 12, 24, and 36 are all common multiples of 3 and 4.
    • To add fractions with different denominators, you must first find a common multiple of the denominators.
Advanced Usage

  • "Least common multiple (LCM)": The smallest common multiple shared by two or more numbers.

    • The least common multiple of 4 and 6 is 12.

  • Conceptual Use: The idea extends beyond simple integers to algebraic expressions, where one finds common multiples of polynomials.

Variants and Related Words

  • Multiple (n): A number that can be divided by another number without a remainder.

    • 20 is a multiple of 5.

  • Least Common Multiple (LCM) (n): The smallest common multiple of two or more numbers.

  • Lowest Common Multiple (LCM) (n): Another term for Least Common Multiple.
Synonyms
  • Shared multiple: A less common but descriptive synonym.
  • Common product: Occasionally used in educational contexts to conceptualize the idea.
Antonyms
  • There is no direct antonym for "common multiple." However, a prime number is a number with no positive divisors other than 1 and itself, which is a contrasting concept as it has very few multiples in common with other numbers.
Related Phrases

  • "Find the common multiple": A standard instructional phrase in mathematics.

    • The first step is to find a common multiple for the denominators 5 and 7.

  • "Have a common multiple": Describes the relationship between a set of numbers.

    • Do the numbers 8 and 12 have a common multiple less than 50?
common multiple

A student circles the common multiple on a math worksheet.

Noun
  1. an integer that is a multiple of two or more other integers

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