When to find the greatest common factor, and when to find the least common multiple

Definition of the greatest common factor Let us say that it is the greatest common factor with if it satisfies the following two conditions:

1), (oral: i.e., the common factor of and);

2) As long as it is satisfied, there is (oral: that is, the factor that any common factor of and is a factor).

When AND is not all zero, for each, is also the greatest common factor of AND . So the greatest common factor of two polynomials is not unique. If the reciprocal of the first coefficient is taken, it is the first greatest common factor of and and is denoted as.

Because any two greatest common factors of and are divisible by each other, and the first polynomial divisible by each other is equal, the first greatest common factor of and is unique.

Definition of Least Common Factor The polynomial in is called the least common multiple of yes if it satisfies:

1), that is, is the common multiple of with;

2) All the polynomials that satisfy must be satisfied, i.e., the multiple of any common multiple of and is.

Obviously, when there is a zero polynomial with them, their least common multiple is also a zero polynomial. When the sum is not zero, their least common multiple is also not zero. We use the first least common multiple to denote them.

It's very detailed.

Good luck with your learning and progress.

Multiples are common multiples, or common multiples. For example, 6 is a common multiple of 2 and 3. The least common multiple refers to the smallest of the common multiples. Let's take 2 and 3 as examples, 6 is its least common multiple, its common multiple and so on.

Answer: When using short division to find the greatest common factor and the least common multiple of two numbers, divide from the minimum prime factor common to the two numbers and continue to divide until the two quotients obtained by the division are co-primed.

For example, find the greatest common factor and the least common multiple of 12 and 18.

Using short division to find the greatest common factor or least common multiple of two numbers, these two numbers are generally divided by their common factors, and divided until the resulting two quotients have only a common factor of 1. Multiply all the divisors to get the greatest common factor of these two numbers; Multiply all the divisors by the last two quotients to get the least common multiple of these two numbers.

For example, use short division to find the greatest common factor and the least common multiple of 18 and 24.

2 18 24 ……Divide by the common factor 23, 9, 12 ...... at the same timeDivide by the common factor 33 4 ...... at the same timeDivide until the two quotients have only a common factor of 1.

Multiply all the divisors to get:

The greatest common factor of 18 and 24 is 2 3 6, which can be expressed as (18,24) 2 3 6.

Multiply all the divisors by the last two quotients to get the least common multiple of 18 and 24 is 2 3 3 4 72, which can be expressed as [18,24] 2 3 3 4 72.

To add that if these numbers cannot be found by short division the greatest common factor and the least common multiple (e.g., 9 and 4), the greatest common factor is 1 and the least common multiple is their product (36 for 4 and 9).

Short division. Multiplying the numbers on the left side is the greatest common factor, and multiplying the numbers on the left side with the bottom side is the least common multiple.

First short division, with the division of the prime number, divide to their mutual prime (only the common factor 1 on the line) the least common multiple to multiply the left and the following are multiplied, and the greatest common factor only needs to be multiplied by the prime number on the left, I hope to adopt, the adoption rate is too low, ** a lot of things can not be bought, although I am just a student, hehe.

To find the greatest common factor of 3 numbers, using short division, you must find the common factor of the three numbers, and then multiply the divisor.

The least common multiple should be divided until the three quotients are mutually primitive, and then all the divisors and the three quotients should be multiplied.

The greatest common factor does not need to be reduced, and the least common multiple 2 and 4 need to be reduced by 2 until the two cannot be reduced to each other.

Multiply the greatest common factor by one side.

Multiply the least common multiple by one turn.

Using short division, the addition of the numbers on the left is the greatest common factor. The bottom is the least common multiple.

Multiplying the left and bottom together is the least common multiple.

Methods are all methods, simple is simple, and short division is short division.

There's no way to express it, you can't do anything about it, because there's no way to express it.

.........I don't know, well, bye-bye.

When using short division to find the greatest common factor and the least common multiple, if it is two numbers, you can use short division to push down with the factors they have in common until the last two numbers are completely homogeneous (there are no other common factors except one). The greatest common factor is the product of the factors common to two numbers, and the least common multiple is the product of the greatest common factor of the two numbers multiplied by the last two coprime numbers.

When the short division method is used to find the greatest common factor and the least common multiple of three or more numbers, the greatest common factor is found according to the method of finding the greatest common factor of two numbers. For example, when the last number of coprime is , it should continue to divide down, 4 and 2 continue to divide by the common factor 2, 5 does not move, and moves down, and finally the number of coprime becomes two pairs of coprime and coprime .

abc is a non-zero natural number, and a is divided by b=c, then, the least common multiple of a and b is (a) and the greatest common factor is (b).

Parentheses are expressions, and the greatest common cause uses parentheses (18 27) = 9

The least common multiple is in parentheses [18 27] = 54

For example, find the greatest common factor and the least common multiple of 20 and 56.

Greatest common factor: 2 2=4

Least common multiple: 2 2 5 2 7 = 280

Short division, the product of all the numbers near the left, is the greatest common factor, and the product of the numbers on the left and below is the least common factor.

Short division, oops, you're stupid.

You use short division.

For example, 6 and 18 are divided by a factor 2 that they have in common, and the two numbers are divided by 3 and 9 respectively, and then there is the same factor 3, and then divided by 1 and 3 respectively, they don't have the same factor, and that's fine.

Note: The divisor must be the common factor of all numbers, you calculate a few steps to multiply the corresponding number, and in the end there is only the common factor 1, so you don't need to divide it anymore. Sometimes you can do it all in one step, and you think that the divisor is the greatest common factor.

If there is no common factor in the first place, then their greatest common divisor is 1, and the least common multiple is their product.

Least common multiple: Multiply the divisor of each time by the final quotient (blue box) Greatest common divisor: Multiply the divisor of each time (red box).

Think for yourself, thank you!

There is no formula for finding the greatest common divisor and the least common multiple.

Remove each number with the common divisor of these numbers, then remove with the common divisor of the partial numbers, and make the indivisible.

The number of is moved down, and it is divided until every two numbers in all quotients are coprime.

, and then multiply all the divisors by the quotient, and the resulting product is the least common multiple of these numbers.

All non-zero natural numbers.

The least common factor.

is 1, and the number of multiples of a number is infinite, so there is no greatest common multiple. Therefore, we often encounter the need to seek the great cause and the small common cause. There are many ways to find the greatest common factor and the least common multiple, the most common and used is short division.

When using short division to find the least common multiple, the difference between finding the greatest common factor is that as long as two numbers are divisible by the same number, they must continue to divide until the quotient is mutually qualified.

1.Find the least common factor of two numbers, divide the column short, and remove these two numbers with the least common factor to get the two quotients.

2.Find out the least common factor of the two quotients, and use the least common factor to remove the two quotients to obtain a new level of two quotients.

3.And so on until the two quotients are coprime numbers.

4.Multiply all the common factors and the last quotient of the two to give the product the least common multiple of the original two.

Example; Find the least common multiple of 48 and 42. Solution:

The two numbers are neither co-prime nor multiples, so they are continuously removed by the prime factors common to these two numbers (generally starting from the smallest), and divided until the resulting quotient is co-prime, and then all the divisors are multiplied by the last two quotients

A box of chocolates is divided equally among six, eight or 12 children and there are no left, how many pieces are there in this box of chocolates?

For example, 50, 60|10---5,6 least common multiple = 5x6x10 = 300That is, find the common divisor of several numbers until you can't find them, and then multiply these numbers.

Belch. It's detailed. Go back and get in touch. After discovering the pattern in the middle, it will become very simple.