Multiplication means that one integer can be divisible by another integer, and this integer is a multiple of another integer. For example, 15 can be divisible by 3 or 5, so 15 is a multiple of 3 and 5.

The quotient obtained by dividing a number by another number, such as a÷b=c, means that A is a multiple of B, and a number has countless multiples, indicating that the set of multiples of a number is infinite. Note that you can't call a number a multiple alone, you can only say who is a multiple of who. Multiplication refers to the quantitative relationship, which is based on the concept of multiplication and division.

Multiplication is the relationship between exponent and number, which is based on the concept of divisibility. For example, 30 is divisible by 6, and 30 is a multiple of 6. It can be seen that "multiplicity" cannot exist independently (with specific directivity), and the form of logarithm has special requirements (it must be an integer). At the same time, 30 is five times that of 6, because 6×5 = 30, "6×5" is five times that of 6.

Therefore, from this perspective, the meaning of "duo" should be broader than that of "duo", and the latter can be regarded as a manifestation of the former under certain circumstances. The common multiple of two or more integers is called their common multiple. The least common multiple of two or more integers is called their least common multiple.

Method of judging multiple

1. prime factor decomposition: this number is decomposed into the product of several prime factors. If several prime factors are divisible by a given number, then this number is a multiple of the given number. For example, to judge whether 12 is a multiple of 3, we can decompose it into 2×2×3 and get three prime factors 2 and 3, of which 3 can be divisible by 3, so 12 is a multiple of 3.

2. One-by-one test method: starting from 1, test whether each integer can be divisible by a given number one by one until an integer that can be divisible is found. For example, to judge whether 14 is a multiple of 5, we can test whether 1, 2, 3, 4, 5 and other integers can be divisible by 14 one by one until we find that the integer 5 can be divisible by 14.