Least common multiple and maximum Common Divisor

Minimum Public multiple
The public multiples of several numbers are called the Public multiples of these numbers, and the smallest one is called the minimum public multiples of these numbers.
Minimum Public multiple:
Square brackets are commonly used in mathematics. For example, [, 20] is the minimum public multiple of 12, 18, and 20.

Method of least common multiple:

There are two methods to calculate the least common multiple of several natural numbers:
(1) decomposition prime factor method. First, we break down these numbers into prime factors, and then combine all their public prime factors with several public prime factors and the unique prime factors of each number, the product is the least common multiple of them.
For example, for [, 20], because 12 = 2 ^ 2 × 3, 18 = 2 × 3 ^ = 2 ^ 2 × 5, the public prime factor of three numbers is 2, the public prime factor of two numbers is 2 and 3, and the prime factor of each number is 5 and 3. Therefore, [12, 18, 20] = 2 ^ 2 × 3 ^ 2 × 5 = 180. (Short Division calculation is available)

(2) Public method. Because the product of the two numbers is equal to the product of the maximum and least common multiples of the two numbers. That is, (a, B) × [a, B] = A × B. Therefore, to obtain the least common multiples of two numbers, you can first find their maximum common divisor, and then use the above formula to find their least common multiples.
For example, if [180] is used, [] = 18 × 20 then () = 18 × 20 then 2 =. Calculate the least common multiples of several natural numbers. You can first find the least common multiples of two numbers, and then find the least common multiples of the least common multiple and the third number, and find them in sequence until the last one. The minimum public multiple obtained at the end is the minimum public multiple of the desired number.

Maximum common approx.
It refers to the largest of the several integers in total.

For example, the common dikes of 12 and 30 are: 1, 2, 3, and 6, where 6 is the maximum common dikes of 12 and 30.

There are two ways to find the maximum common divisor of two integers:

* The two numbers are decomposed into quality factors, and the same items are taken out to multiply them.
* Phase division (extended version)

Relationship with least-common (LCM): gcd (a, B) × lcm (a, B) = AB

The least common factor of two integers can be used to calculate the least common factor of two numbers, or to reduce the score to the simplest score.

The distribution law exists in the least common factor and least common multiple of the two integers:

* Gcd (A, lcm (B, c) = lcm (gcd (a, B), gcd (a, c ))
* Lcm (A, gcd (B, c) = gcd (LCM (a, B), lcm (a, c ))

In coordinates, the points (0, 0) and (A, B) are connected by the number of points in the integer coordinates (except (0, 0) is gcd (A, B ).

 

This article is from the csdn blog. For more information, see http://blog.csdn.net/jqandjq/archive/2009/04/02/4042843.aspx