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The greatest common divisor and least common multiple
1.c ++ comes __gcd (int m, int n) function can be used to greatest common divisor;
2. least common multiple = m * n / a greatest common divisor;
Further greatest common divisor of two methods
M1. Euclidean (Euclidean algorithm)
M2. Euclidean subtractor (Decreases Technique)
See also the GCD
Pure violence enumeration can do
The greatest common divisor multiple numbers
Least common multiple of the number of
First seek the greatest common divisor of two numbers, then find the least common multiple of two numbers according to the greatest common divisor of two numbers, and then seek the least common multiple and greatest common divisor another new number, then the maximum seek common divisor least common multiple, and so on ......
LCM&GCD
Suppose gcd (a, b) = x , lcm (a, b) = y, can be obtained: GCD LCM A = B, i.e., X Y = A B, with the dividing x2, have y / x = (a / x ) (B / X), so that y1 = y / x, a1 = a / x, b1 = b / x, then A1 = Y1 B1, and a1∈ [1, y1]. After this simplification, then traverse [1, sqrt (y1)] (only to traverse to the root number y1) to find satisfying gcd (a1, b1) == 1, the update answers.
Special attention sentence a1 * a1 = y case, the answer +1; otherwise answer +2.
NOTE:
1.gcd (A, B) = X, LCM (A, B) can be introduced Y = A B X = Y; but the reverse is not introduced;
2. The least common multiple of the greatest common divisor must be;
3. it is equal to the number of number gcd (a, b) established with gcd (a / x, b / x) a;
4.gcd (a, B) X is = GCD (m a, m B) = m * X; gcd (a / m, b / m) = x / m;
Cute gcd
Takagi students factor
First seek the greatest common divisor of two numbers, and then seek the greatest common divisor of all factors, that is, all factors of two numbers.
