# Author's software

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Least common multiple

Writing functions:

noc(a, b, c,...,n)

Finds from the least common multiple integers a, b, c,...,n.

The mathematical function known as the "least common multiple" (LCM) is one of the fundamental operations in algebra and mathematical analysis. It is used to find the smallest number that is divisible without remainder by two or more given numbers.

The definition of LCM can be formulated as follows: let m and n be two integers. The LCM between them, denoted as LCM(m,n), is the smallest integer that is divisible without remainder by both m and n.

The mathematical symbol used to denote LCM is a common parenthesis with numbers inside, for example, NOC(m,n). In some cases, when it is obvious which numbers are in question, the indexes may be omitted.

Therefore, in order to calculate the LCM(m,n), the following steps must be performed:

1. Find all the prime factors of each of the numbers m and n.

2. Raise each prime factor to a power equal to the maximum degree to which it occurs in any of the numbers.

3. Multiply all the values obtained.

The application of LCM covers a wide range of areas. In the context of arithmetic and algebra, the smallest common multiple is used to simplify fractions and solve equations. For example, to sum fractions with different denominators, it is necessary to find their common denominator, which will be equal to the NOC of the original denominators. This allows you to make the operation of adding fractions simpler and more convenient.

In physics, LCM is used to calculate periodic processes such as vibrations and waves. It can be used to determine the total period of two or more functions, which allows you to predict the behavior of the system in the future.

The LCM can also be used to determine the time of occurrence of events and the schedule. For example, to determine whether two events will coincide in the schedule, you need to find the number of intervals between them. If this number is common to both intervals, then the event will occur simultaneously.

In conclusion, the smallest common multiple is an important mathematical function used in various fields ranging from arithmetic and algebra to physics and planning. Its application makes it possible to simplify complex operations, identify periodic processes and predict temporary events. Understanding and using this function is an important element in mathematics and its applications.

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