For example, find the greatest common factor and the least common multiple of 12 and 18.
Method 1: Screening method.
The factors of 1 and 12 are 1, 2,3,4,6, 12.
12 includes 1, 2, 3, 6.
The greatest common factor of 12 and 18 is 6.
2. The multiple of 18 is18,36,54,72.
Of the multiples of 18, 36,72 is a multiple of 12.
The least common multiple of 12 and 18 is 36.
Method 2: factorization factor method.
12=2×2×3, 18=2×3×3。
The greatest common factor of 12 and 18: 2× 3 = 6; Least common multiple: 2× 3× 2× 3 = 36.
Method 3: Short division.
The greatest common factor of 12 and 18: 6; Least common multiple: 6× 2× 3 = 36.
The solution of the greatest common factor;
Multiply the common prime factor by decomposing the prime factor.
Find the greatest common divisor of two numbers by short division.
Special case: If two numbers are coprime, then their greatest common divisor is 1.
If the smaller number of two numbers is the divisor of the larger number, then the smaller number is the greatest common divisor of these two numbers.
Least common multiple method;
By decomposing prime factors, these two common prime factors are multiplied by their unique prime factors.
Find it by short division.
Special case: If two numbers are prime numbers, then the product of these two numbers is their least common multiple.
If the larger number of two numbers is a multiple of the smaller number, the larger number is the least common multiple of the two numbers.
The benefits of learning mathematics
1. Mathematics is the foundation of all sciences, and all major scientific and technological progress is closely related to mathematics. Without mathematics, there would be no computers, televisions and space shuttles, and there would be no such colorful life today.
2. Mathematics is a tool discipline, which is the basis of learning other disciplines and also a discipline to improve people's judgment, analysis and understanding.
Mathematics is not only a science, but also a universally applicable technology. It is the door and key to science. Learning mathematics is a very important measure to make oneself rational, and mathematics itself has its fun.