if a number a is divisible by a number b, a is called a multiple of b and b is called a divisor of a. divisors and multiples both express the relationship between one number and another number and cannot exist alone. for example, we can only say that 16 is a multiple of a certain number and 2 is a divisor of a certain number, but we cannot say in isolation that 16 is a multiple and 2 is a divisor.

"multiple" and "multiple" are two different concepts. "multiple" refers to the quotient of dividing two numbers, which can be an integer, a decimal or a fraction. "multiple" is just a concept of a number within the range of divisibility of a number, relative to "divisor", which represents a number that can be divisible by a certain natural number. 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 one is 4. 4 is the greatest common divisor of 12 and 16. it is generally recorded as (12, 16) = 4. the largest of 12, 15, and 18 the common divisor is 3, recorded as (12, 15, 18) = 3.

the common multiples of several natural numbers are called the common multiples of these numbers. the smallest one among them is called the smallest common multiple of these numbers, and it 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 them is 12 , generally recorded as [4, 6]=12. the least common multiple of 12, 15, and 18 is 180. recorded as [12, 15, 18] = 180.