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?

Noun

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