lowest common multiple
Học thuậtThân thiện
The teacher writes the lowest common multiple of 12 and 18 on the chalkboard.
Definition
- 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.
The teacher writes the lowest common multiple of 12 and 18 on the chalkboard.
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