Fractions Greatest Common Divisor Least Common Multiple Calculator

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If a is divisible by b, a is called a multiple of b, and b is called a divisor of a. Both divisors and multiples represent the relationship between one number and another, and cannot exist independently. For example, we can only say that 16 is a multiple of a number, and 2 is a divisor of a number, but we cannot say that 16 is a multiple and 2 is a divisor in isolation.

"Times" and "multiples" are two different concepts. "Times" refers to the quotient of two numbers, which can be an integer, decimal or fraction. "Multiples" is just a concept of a number within the range of divisibility of a number, relative to "approximate divisor", which means a number that can be divided by a natural number, and it must be a natural number.

The common divisors of several natural numbers are called the common divisors of these numbers; the largest one among them is called the greatest common divisor of these numbers. For example: the common divisors of 12 and 16 are 1, 2, and 4, and the largest one among them is 4. 4 is the greatest common divisor of 12 and 16, which is generally recorded as (12, 16) = 4. The greatest common divisor of 12, 15, and 18 is 3, which is recorded as (12, 15, 18) = 3.

The common multiples of several natural numbers are called the common multiples of these numbers, and the smallest one among them is called the smallest one of these numbers, which is called the least common multiple of these numbers. For example: the multiples of 4 are 4, 8, 12, 16, ..., the multiples of 6 are 6, 12, 18, 24, ..., the common multiples of 4 and 6 are 12, 24, ..., the smallest one is 12, which is generally recorded as [4, 6] = 12. The least common multiple of 12, 15, 18 is 180. It is recorded as [12, 15, 18] = 180.