Fractions Greatest Common Divisor Least Common Multiple Calculator

If number a is divisible by number 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 number, 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, a decimal or a fraction. "Multiples" is just a concept of a number within the scope of the divisibility of a number, relative to "divisors", 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, the largest of which is 4. 4 is the greatest common divisor of 12 and 16, generally recorded as (12, 16) = 4. The greatest common divisor of 12, 15, and 18 is 3, 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 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 of which is 12, generally recorded as [4, 6] = 12. The least common multiple of 12, 15, and 18 is 180. It is recorded as [12, 15, 18] = 180.