"Least common multiple" Method

I. list multiple methods

　　

The minimum public multiples of two numbers are required. You can first list the multiples of each number, such as 1, 2, and 3 ...... Then find out their least common multiples. In example 1, calculate the minimum public multiple of 18 and 24. Solution: The multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144 ...... Multiples of 24: 24, 48, 72, 96, 120, 144 ...... Therefore, the concept [] = 72 is determined by the minimum public multiple. The enumerated multiples method is applicable to finding the least common multiples of two or more numbers. This method is generally used to describe the concepts of the Public multiples and least common multiples of several numbers.
　　

Ii. decomposition prime factor method
　　

The minimum public multiple of two numbers is required. You can separate each number into a prime factor and write it into a standard factorization formula. To make the two numbers have the same prime factor, You can multiply the zero power of a prime factor, retrieve all the public prime factors, and take a greater value for each index with the same prime factor. At last, the exponent power of the retrieved prime factor is multiplied, and the product is the minimum public multiple of the two numbers. In Example 2, the minimum public multiples of 2940 and 756 are obtained. Solution: Because 2940 = 22 × 3 × 5 × 72,756 = 22 × 33 × 50 × 7,
Therefore, [2940,756] = 22 × 33 × 5 × 72 = 26460.
The Factorization prime factor method is suitable for finding the least common multiple of two or more numbers.
　　

Iii. Extraction of Public factor
　　

In Example 3, calculate the least common multiples of 108 and 204.
Solution: [108,204] = 4× [27,51] = 4× 3× [9,17] = 1836
The extraction public factor method is suitable for finding the minimum public factor of two or more numbers. The method steps are as follows: (1) extract the maximum public factor of these numbers first and extract them in multiple times (the resulting commodity mutual quality, but it is not necessarily mutual quality); (2) extract the public factor from the non-mutual quality vendors, and write down the other vendors until the mutual quality of each other is reached; (3) finally, the number extracted and the number of each commodity are multiplied, and the product is the minimum public multiple of these numbers.
　　 　　

Iv. Scoring Method
　　

The minimum public multiple of two numbers is required. You can first write the two numbers into the score form, and then divide the score into the simplest score ), the numerator of the original score is multiplied by the denominator of the simplest score (or the denominator of the original score is multiplied by the numerator of the simplest score). The product is the least common multiple of the two numbers.
In Example 6, calculate the minimum public multiple of 12 and 16.
Solution: Because 12/16 = 3/4,
Therefore, [] = 12 × 4 = 48 (or 16 × 3 = 48 ).
　　

V. Proportional Method
　　

The minimum public multiple of two numbers is required. You can regard these two numbers as the first and last items of a ratio, and then convert them into the simplest integer ratio to form a ratio, the product (or outer product) of the inner of this proportion is the least common multiple of the two numbers.
In Example 7, calculate the least common multiples of 18 and 48.
Solution: Because =,
Therefore, [144] = 48 × 3 = 144 (or 18 × 8 = ).
Note: The theory for solving proportional, approximate, and cross-phase multiplication is the same, but the writing format is different.
　　

6. Expansion of large (small) Numbers
　　

The minimum public multiple of two numbers is required. The larger number is not a multiple of the decimal number. You can increase the larger number (or decimal number) by 2 times, 3 times, and 4 times ...... The number obtained after a small expansion to a certain multiple is exactly a multiple of a decimal number (or a large number), then this number is the minimum public multiple of the two numbers.
In Example 8, calculate the minimum public multiples of 8 and 18.
Solution: Because 18 × 2 = 36, 36 is not a multiple of 8:
18 × 3 = 54,54 is not a multiple of 8;
18 × 4 = is a multiple of 8;
So [8, 18] = 72.
The big (small) number expansion method is applicable to finding the minimum public multiple of two or more numbers.
　　

VII. Special Data Query
　　

The minimum public multiple of two numbers is required. If the large number is a decimal multiple, the large number is the minimum public multiple of the two numbers. If the two numbers have only the public factor 1, the product of these two numbers is their least common multiples. If the two numbers are the same, their least common multiples are themselves. The special number method is applicable to finding the least common multiple of two or more numbers. When the larger number is a multiple of the other numbers, the larger number is the least common multiple of these numbers; if there are two or two numbers, the product of these numbers is their least common multiple.
　　

8,Maximum public factor division Product Method
　　

The minimum public factor of two numbers is required. First, the maximum public factor of the two numbers is obtained, and then the product of the two numbers is removed by the maximum public factor. The quotient obtained is the minimum public multiple of the two numbers.