There are several common multiples of four and six, and what is the smallest common multiple

There are an infinite number of common multiples of 4 and 6, of which the smallest common multiple is 12.

Common multiples: Refers to two or more natural numbers that are common multiples if they have the same multiple. There are infinite multiples of common multiples of any two or more natural numbers because the number is infinite.

The least common multiple, the smallest of all common multiples of these numbers, is the least common multiple of these numbers.

There are generally two ways to find the least common multiple: one is prime factor factorization, and the other is short division.

1. Prime factor decomposition method.

The product of several numbers is the least common multiple of these numbers, and then all the common prime factors and unique prime factors in each number are extracted and multiplied.

For example, this problem finds the least common multiple of 4 and 6: first decompose the prime factors, and get 4=2 2,6=2 3,4 and all the common prime factors of 6 are 2, 4 The unique prime factor is 2 (4 has two prime factors 2, one of which is common and the other is unique), the unique prime factor of 6 is 3,2 3 2=12, 12 contains all the prime factors of 4, and also contains all the prime factors of 6, and 12 is the smallest of the common multiples of 4 and 6, so the least common multiple of 4 and 6 is 12.

2. Short division.

To find the least common multiple by short division, first use the common divisor of these numbers to remove each number, and then use the common divisor of the partial numbers to remove, and remove the indivisible numbers until every two numbers in all quotients are coprime, and then multiply all the divisors and quotients, and the resulting product is the least common multiple of these numbers.

The essence of short division is the prime factor factorization method, but the prime factor is decomposed by short division symbols.

The short division sign is the division sign reversed. Short division is to write the prime factor common to two numbers where the divisor is written in division, and then drop the quotient of the two numbers divisible by the common prime factor, and then divide, and so on, until the result is coprime (the two numbers are co-primed).

When calculating multiple numbers with short division, the factors that exist in any two of them are calculated, and the other numbers that do not have this factor fall as they are. Until every two remaining are mutual. Find the least common multiple and multiply it by one circle.

This question is answered by short division as follows:

There are [innumerable] common multiples of four and six.

The smallest common multiple of which is:

The least common multiple of 4 and 6.

Yes 12. The process is as follows:

Least common multiple = 2 2 3 = 12

The common multiple of two or more integers is called their common multiple, and the smallest common multiple other than 0 is called the least common multiple of these integers. The least common multiple of the integers a,b is denoted as [a,b], and similarly, the least common multiple of a,b,c is denoted as [a,b,c], and the least common multiple of multiple integers also has the same stool rotten-like mark.

To find the least common multiple of two numbers, first require the least common divisor of the two suspects, the least common divisor of 4 and 6 is two, and then divide four by 2 and divide by 2 and divide by 2 and their least common divisor two, which is their least common multiple, that is, 12.

This problem should be solved by short division, write 46 side by side, they have a common factor of 2, except for 2, there are 2 and 3 respectively, and this finch loses two numbers, and there is no factor, so the least common multiple is 2 times the state, and the state is multiplied by two, and the result is 12

The least common multiple of 4 and 6 is 12

The greatest common factor of 4 and Shengtong faction 6 is 2, and both 4 and 6 are divisible by 1,2, so the greatest common factor is 2.

The common multiples of 4 and 6 are 12, 24, etc., where the least common multiple is 12.

The common factor, also known as the "common divisor". It is an integer that is divisible by several integers at the same time. If an integer is a factor of several integers at the same time, the integer is called their "common factor"; The largest of the common factors is called the greatest common factor.

For any number of positive integers, 1 is always their common factor.

Common multiples are two or more natural numbers that are common multiples if they have the same multiple. The smallest of the common multiples is called the least common multiple of these integers.

Extended Materials

Common Factor Calculation Method:

1.Multiples of relationships.

If the larger number is a multiple of the smaller number, then the smaller number is the greatest common factor for both numbers.

2.Coprime relationship.

Two numbers with a common factor of only 1 are called coprimes. For example, 5 and 7 are coprime numbers.

Note: 1 is a factor of any integer.

Calculation method of least common multiple:

1.Decomposing Prime Factor Method:

First of all, the prime factors of the two numbers are written out, and the least common multiple is equal to the product of the representatives of the prime factors common to all the two numbers and the unique prime factors of each of them.

For example, find the least common multiple of 45 and 30.

The prime factors shared by 30 and 45 are 1 3 and 1 5, while the prime factors unique to 30 and 45 are 3 and 2 respectively. That is, the least common multiple is equal to 2 3 3 5 = 90

Another example is calculating the least common multiple of 36 and 270.

The prime factors that 36 and 270 have are 1 2 and 2 3s, while 36 has a unique prime factor of 2, and 270 has a unique prime factor of 3 and 5.

The least common multiple is equal to 2 2 3 3 3 5 = 540

2.Multiples relationship: If the larger number is a multiple of the smaller number, the higher number is their least common multiple.

The least common multiple of 4 and 6 is 12

The common multiple of two or more integers is called their common multiple, and the smallest common multiple other than 0 is called the impermeable least common multiple of these integers. The least common multiple of the integers a,b is denoted as [a,b], similarly, the least common multiple of a,b,c is denoted as [a,b,c], and the least common multiple of multiple integers is denoted as [a,b,c].

The concept corresponding to the least common multiple is the greatest common divisor, and 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).

The least common multiple of the natural numbers a and b can be denoted as [a, b], and the greatest common factor of the natural numbers a and b can be denoted as (a, b), and when (a, b) = 1, [a, b] = a b. If two numbers are multiples, then their least common multiple is the larger number, and the least common multiple of two adjacent natural numbers is their product.

Least common multiple = product of two numbers Greatest common divisor (cause) number, avoid confusion with the maximum common divisor (factor) problem when solving the problem. Scope of application of least common multiple: addition and subtraction of fractions, Chinese remainder theorem (the correct elimination macro problem has a solution within the least common multiple, and there is a unique solution).

Because, a prime number is a number that is not divisible by numbers other than 1 and its own number; The prime number x to the nth power is only divisible by x to the nth power, 1 and its own number.

The least common multiple of 4 and 6 is 12

The process is as follows:

4=2 2,6=2 3 Least common multiple=2 2 3=12

The common multiple of two or more integers is called their common multiple, and the smallest common multiple other than 0 is called the least common multiple of these integers. The least common multiple of the integers a,b is denoted as [a,b], and similarly, the least common multiple of a,b,c is denoted as [a,b,c], and the least common multiple of multiple integers is also denoted by the same notation.

How to find the least common multiple:

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. In the calculation of the least common multiple, it is necessary to find all the common prime factors and unique prime factors of the three numbers, and finally divide them until they are mutually primary.

Finding the least common multiple:

1. Decompose the prime factor method: first write out the prime factors of these numbers, and the least common multiple is equal to the product of all their prime factors (if there are several prime factors of the same, then compare which of the two numbers has more of the prime factors, and the number of times multiplied by more is boring).

2. Formula method: 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. i.e. (a,b) [a,b]=a b.

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.

The applicable range of the least common multiple is wide

Addition and subtraction of fractions, Chinese remainder theorem (the correct problem has a solution within the least common multiple, and there is a unique solution). The application of the least common multiple to practice is called the least common multiple method. The least common multiple method is a term in statistics that uses the least common multiple of the calculation period of each alternative as the common calculation period of the comparison scheme, and assumes that each or bend scheme is repeated in such a common calculation period.

The least common multiple of 4 and 6 is 12

Least common multiple:

If there is a natural number A that is divisible by the natural number b, then a is said to be a multiple of b, b is a divisor of a, and in the case of two natural numbers, the smallest of the two numbers is a multiple. When calculating least common multiples, the greatest common divisor is usually used to aid the calculation.

If a number is both a and b multiples, then we call the number a and b common, and if the number is the smallest of all the common multiples of a b, then the number is the least common multiple.

2. Common multiples

It refers to the fact that in two or more natural numbers, if they have the same multiple, these multiples are their common multiples.

Multiples of 4: 4, 8, 12, 16, 20, 24,

Multiples of 6: 6, 12, 18, 24, 30, 36, .,

As can be seen from Wang Zhuliang's above list, the common multiples of 4 and 6 include , sleepy wide, sleepy wide, 36 and so on. The least common multiple is the smallest positive integer that is divisible by the width of the trap, i.e., 12.

2. Understanding that 12 is the least common multiple of 4 and 6, we can consider the following:

Among the multiples of 4, 12 is the smallest number that Wang Shuliang can be divisible by 4. Among the multiples of 6, 12 is the smallest number that is divisible by 6. 12 is divisible by both 4 and 6, i.e. 12 is both a multiple of 4 and a multiple of 6.

12 is the smallest positive integer that satisfies both of the above conditions. Therefore, 12 is the minimum common number of chops for 4 and 6.

3. Examples

There are some brick skin chops, the length, width and height are respectively, how to swing, in order to be able to put into a smallest cube.

Solution: Let the least common multiple of be 60, so the minimum cube edge length is 60

Answer: Length: 4 pieces, width: 5 pieces, height: 10 pieces, in order to form a smallest cube.

4. Precautions

There is no maximum common factor and least common multiple, and the greatest common factor (greatest common divisor) and least common multiple only exist in natural numbers.

The process is as follows:

Least common multiple = 2 2 3 = 12

The common multiple of two or more integers is called their common multiple, and the smallest common multiple other than 0 is called the least common multiple of these integers. The least common multiple of the integers a,b is denoted as [a,b], and similarly, the least common multiple of a,b,c is denoted as [a,b,c], and the least common multiple of multiple integers is also denoted as [a,b,c].

The least common multiple of 4 and 6 is 12

Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ,...Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42 ,...Multiples of 4 and 6 are:

12，24，36，…The minimum multiple of public ownership is 12.

The least common multiple of 4 and 6 is 12, calculated method.

Therefore, the least common multiple is 2 2 3 = 4 3 = 12

There are an infinite number of common multiples of 4 and 6, but there is only one least common multiple. There can't be several! The least common multiple of 4 and 6 is 12The common multiple can be ......

Multiples of 4 have ......

Multiples of 6 have ......

So: the least common multiple of 4 and 6 is 12.

The least common multiple of 4 and 6 is 12

Hello! Glad for your question!

Answer: The least common multiple of 4 and 6 is 12.

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4 and 6 have a common factor of 2, so the least common multiple is 2*3*2=12

and 6 have a greater common factor of 2 and a least common multiple of 12. Both 4 and 6 are divisible by 1,2, so the greatest common factor is 2. The common multiples of 4 and 6 are 12, 24, etc., where the least common multiple is 12.