How to calculate chemical formulas, such as least common multiples

First, write out the prime factors of two numbers, and the least common multiple is equal to the product of all their prime factors (if there are several prime factors that are the same, compare which of the two numbers has more of that prime factor, and multiply more times). That is, if there are duplicate prime factors, take the group with the most, and multiply the non-repeating prime factors.

For example, find the least common multiple of 5 and 17.

The different prime factors are 17, which is the prime factor that both of them have, and the least common multiple is equal to 1*5*17=85

Another example is calculating the least common multiple of 36 and 12.

Different prime factors do not. The prime factor of 3 is more in 36, it is two, so it is multiplied twice; The least common multiple is equal to 2*2*3*3=36 and so on.

The least common multiple is equal to 2*2*3*3*3=108

The least common multiple is equal to 2*2*3*3*5*7=1260

jiangkaien1 | 2010-07-28

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An integer can be divisible by another integer, and that integer is a multiple of another integer. For example, 15 is divisible by 3 or 5, so 15 is a multiple of 3 and a multiple of 5. .

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Use homework help to ask with one click, "How to calculate the most." Issue.

Other. If they are mutually primary, the least common multiple is their product, as in this problem.

Vividi | 2010-07-28

If both numbers are prime, the product of the multiplication of the two numbers is the least common multiple, and if both numbers are multiples, the least common multiple is the lesser number.

I thought it was a brain teaser......

I didn't want to answer, but the two upstairs missed and made a mistake, answer: 85 36 108 108 315 420

Method: Decompose the two numbers according to the minimum prime factor, and take the common prime factor of the two numbers and the remaining quality of the other number.

Multiply the factors (you can also multiply two numbers by dividing them by the greatest common divisor of two numbers, which is relatively simple).

For example: 5=1*5, 17=1*17, least common multiple = 5*17

12 = 2 * 2 * 3, 108 = 2 * 2 * 3 * 3 * 3 * 3, least common multiple = 2 * 2 * 3 * 3 * 3 * 3 or = 12 * 108 12

1. If two numbers are coprime.

Then their least common multiple.

It is the product of these two numbers.

2. If there is a multiple relationship between two numbers, then the larger number is the least common multiple of these two numbers.

3. If the two numbers are not coprime and there is no multiples relationship, the larger number can be expanded by 2 times and 3 times in turn、......When you see which number you expand to first, it becomes a multiple of the smaller number first, and that number is the least common multiple of the two numbers.

The concept corresponding to the cardinality of the least common front is the greatest common divisor.

The greatest common divisor of a,b is denoted as (a,b). Regarding the least common multiple and the greatest common divisor, we have this theorem: (a,b)x[a,b]=ab(a,b are integers).

Trim of chemical equations - least common multiple method.

The general practice is to write these numbers separately as the product of prime numbers, which is better than the song wheel tan

Then the same parts of the equation are combined into a prime number, and then multiplied by the remaining prime number.

There is no same part of the above three formulas, only 3, 2*2, 5 are not the same parts, so the least common multiple is 3*2*2*5=60

Similarly, the least common multiple of 6,12,18 is found as follows:

You see, merge the three 2s in the above three formulas into a 2, and the three 3s into a 3, leaving a 2 and a 3, so the multiplication is 2*3*2*3=36

a，b×a，b=a×b。

The property between the greatest common factor and the least common multiple is guessed that the product of two natural numbers is equal to the product of the greatest common divisor and the least common multiple of these two natural numbers.

First, decompose the prime factors of these numbers separately, so that the least common multiple is equal to the product of all the prime factors of the other family. If there are several prime factors that are the same, then compare which number of these numbers has the more prime factors, and if Zhao Chan assumes n to n, then multiply the prime factor n times.

a，b）×[a，b]=a×b。Since the product of two numbers is equal to the product of the greatest common divisor and the least common multiple of these two numbers. So, to find the least common multiple of two numbers, you can first find their greatest common divisor, and then use the above formula to find their least common multiple.

Property between the greatest common factor and the least common multiple: The product of two natural numbers is equal to the product of the greatest common divisor and the least common multiple of these two natural numbers. The calculation of the least common multiple should find out the common prime factor and the unique prime factor of the three numbers, and finally divide them until they are two and two mutual qualities.

1. First, use the prime factor (or divisor) common to three numbers to remove it continuously;

2. When there is no common quality factor for the three numbers, remove it with the common quality band tremor factor of two of the numbers;

3. Divide until the last three quotients are mutually qualitative;

4. Multiply all the divisors by the final quotient.

Example: Find the least common multiple of . <>