Common multiple refers to the smallest positive integer that can be divisible among multiple numbers at the same time, that is, the multiple of these numbers.
For example, the common multiple of the numbers 2, 4 and 6 is 12, because 12 can divide these three numbers at the same time.
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When we need to calculate two or more numbers, if they have common multiples, we can operate according to the common multiples, such as finding their greatest common factor or smallest common multiple. Therefore, common multiple is an important concept in mathematical operation, which is widely used in many fields, such as arithmetic, algebra, number theory and so on.
In practical application, finding the least common multiple is a very common operation, such as simplifying fractions, solving equations, solving periodic problems and so on. A common method is to find the common factor of these numbers by decomposing prime factors, and then find the product of these common factors to get their least common multiple.
In addition, there is another method called "polyphase subtraction", which can be used to find the greatest common divisor and the least common multiple. The basic idea of this method is to subtract two numbers step by step until they are equal, and then this equal number is their greatest common divisor.
Finally, the product of the greatest common divisor and the original two numbers can be divided by the greatest common divisor to get their least common multiple.
In a word, common multiple is a basic and important concept in mathematics. Understanding common multiples can help us better understand mathematical concepts and their applications, and also enable us to deal with practical problems more efficiently.
In the problem of algorithm class, if the least common multiple of a group of numbers is required, a common method is to decompose these numbers into prime factors, find out all their common prime factors, and multiply these prime factors to get their least common multiple. This method is simple and feasible in practical application.
In addition, solving the least common multiple is also a very important problem in computer science. In the case of two numbers, their greatest common divisor will be calculated by division or Euclid algorithm, and then the least common multiple will be calculated according to the greatest common divisor. However, when it is necessary to calculate the least common multiple of multiple numbers, this method will be more troublesome and time-consuming.
So when there are multiple numbers, we usually design a more efficient algorithm to calculate their least common multiple.