How to find the greatest common factor and the least common multiple of 9 and 36

The greatest common factor of 9 and 36.

is 9, the least common multiple.

It was 36. The method of finding the greatest common factor and the least common multiple is categorized:

1. Special circumstances:

1. The greatest common factor is the smaller number, and the least common multiple is the larger number. (e.g.; The greatest common factor of 6 and 12 is 6, and the least common multiple is 12. ）

2. The greatest common factor of two numbers of the coprime relationship is 1, and the least common multiple is their product. (e.g., when the greatest common factor of 5 and 7 is 1, the least common multiple is 5 7 = 35).

Second, the general situation:

1 Finding the Greatest Common Factor:

Enumeration, single enumeration, factorization of prime factors, short division.

Division method.

Enumeration: For example, find the greatest common factor of 18 and 27.

Find all the factors of the two numbers first.

The factor of 18 has

The factor of 27 has

Find the common factor of the two numbers again:

Finally, find out the greatest common factor:

Single enumeration: For example, find the greatest common factor of 18 and 27.

Find out the factor of one of the numbers first: the factor of 18 has

And then look for the factors that are the other factors, which are the factors of 27.

Finally, find out the greatest common factor:

Short division (universal method):

2. Find the least common multiple:

Enumeration, single enumeration, multiples of large numbers, factorization of prime factors, or short division.

Enumeration: For example, find the least common multiple of 18 and 12.

Find the multiples of these two numbers in descending order:

Multiples of 18

Multiples of 12

Find the least common multiple of the two numbers again:

Single enumeration: e.g., find the least common multiple of 18 and 12.

Find out the multiple of a number first:

There is a multiple of 18

Then find the multiple of which of these multiples is the multiple of another number in the order from smallest to largest, and find the least common multiple:

Multiplication of large numbers: For example, find the least common multiple of 18 and 12.

Large number multiples method (more used in practice):

Double the larger number (starting at 2x) and see if the result is a multiple of another number after each doubling until you find the least common multiple.

For example, find the least common multiple of 18 and 12. 18 can be doubled: 18 2 = 36, and 36 is a multiple of 12, so 36 is the least common multiple of 18 and 12.

Short division (universal method): Divide both numbers by a prime number (divisible) at the same time

For example, to find the least common multiple of 18 and 12, divide 18 and 12 by prime 2 at the same time, and then divide by prime 3 at the same time, and divide the two quotients to be coprime.

The common factor is only 1).

The factor of 24 has

The factor of 36 has

The greatest factor of the same is 6, which is their greatest common factor.

Multiples of 24 have .

Multiples of 36 have .

The smallest multiple of the same is 72, which is their least common multiple.

The greatest common factor of 6 and 9 is 3, and the least common multiple is 18.

The algorithm is: Decompose the prime factors of two numbers separately:

Multiply all the common prime factors, and the product is the greatest common factor of the two numbers, because the common prime factors of 6 and 9 are only 3, so the greatest common factor is 3;

Multiply all the prime factors together, and the resulting product is the least common multiple of the two numbers (if two numbers have the same prime factor, multiply only the one with more occurrences): 2 3 3 = 18, so the least common multiple is 18.

Analysis: Because 36 9 = 4, that is, 36 and 9 are multiples, when two numbers are multiples, the larger number is the least common multiple of these two numbers, and the smaller number is the greatest common factor of these two numbers; Because 36 9 = 4, that is, 36 and 9 are multiples, the greatest common factor of 9 and 36 is 9, and the least common multiple is 36; So the answer is: Reviews:

This question mainly examines the finding of the greatest common factor of two numbers: the two numbers are multiples, the greatest common factor is the smaller number, and the larger number is the least common multiple of the two numbers

The greatest common factor for 36 and 49 is 1 because it has only one common factor, which is themselves.

Their least common multiple is 49 because 49 is the smallest positive integer among them, and 49 is their product.

To find the greatest common factor of two numbers in hailstorm, you can use short division, i.e., divide the two numbers by their greatest common divisor, and the quotient obtained is their greatest common factor. For these two numbers, the greatest common divisor is 1, so their greatest common source Sun factor is also 1.

To find the least common multiple of two numbers, you can use long division, which divides the two numbers by their greatest common divisor respectively, and the resulting quotient plus 1 is their least common multiple. For these two numbers, the greatest common divisor is 1, so their greatest common divisor is also 1, so their least common multiple is 49.

Solution: The factors of 36 are 1, 36, 2, 18, 3, 12, 4, 9, and 6.

The factor of 49 is 1,49,7. Knowing the world.

Since the common factors of 36 and 49 are only 1, the greatest common factor is 1: the least common multiple is 36 49 = 1764.

Because 36 9 = 4, that is, 36 and 9 are multiplied by the old number relationship, the greatest common factor of 36 and 9 is 9, and the least common multiple is 36; Dates are withered.

So the answer is:

<> common factor and common multiple envelope are done by short division, 30 The greatest common factor is also the common factor, and it can be seen from the above figure that the common factor of these three numbers is only 3, so the greatest common factor is 3. It is important to remember when finding the common factor of three numbers, except that (three quotients can be mutually qualified)!

As can be seen from the Tanling diagram, their least common multiple is 90.

When finding the least common multiple of three numbers, it is also important to keep in mind that when dividing to the final result, the relationship between them is (two pairs of co-primes).

6, 9 and 30 maximum common factor = 3, manuscript celery least common multiple = 2x3x3x5 = 6x15 = 90

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Question : What is the least common multiple and the greatest common factor of 6,9,30?

Lcm.

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 whole-life mills is also marked with the same notation.

The concept corresponding to the least common multiple is the maximum common divisor search for buckets, 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 both integers).

Greatest common factor.

The greatest common factor, also known as the greatest common divisor or greatest common factor, refers to the largest of the common divisors of two or more integers. The greatest common divisor of a,b is denoted as (a,b), similarly, the greatest common divisor of a,b,c is denoted as (a,b,c), and the greatest common divisor of multiple integers is also denoted by the same notation. There are many ways to find the greatest common divisor, the common ones are prime factor factorization, short division, tossing and turning division, and more derogation.

The concept corresponding to the greatest common divisor is the least common multiple, and the least common multiple of a, b is denoted as [a, b].

Examples of least common multiples and greatest common factors.

Example 1: Hu Song 2,4 : Least common factor = 4, Greatest common factor = 2

Example 2 2,4,6 : Least common multiple=12, Greatest common factor=2

Example 3 2,4,6,8 : Least common multiple=24, Greatest common factor=2

Decomposition with prime numbers.

6=2x39=3x3

30=2x3x5 so.

Least common multiple = 2x3x3x5 = 90

Greatest common factor = 3

Derived. The least common multiple of 6,9,30 = 90, and the greatest common factor = 3

The least common multiple of 6,9,30 = 90, and the greatest common factor = 3

First find their factors:

The factor of 6 is ;

The factor of 9 is ;

The factor of 30 is , bright and ready .

Their greatest common factor is 3, and 3 is the largest of their common factors.

Their least common multiple is 90 because 90 is the smallest of their common multiples.

The greatest common factor is the number that is the largest of two or more factors.

The least common multiple is the smallest of two or more common multiples.

The greatest common factor is 3; The least common multiple is 90.

Analysis: Because 36 9 = 4, that is, 36 and 9 are multiples, when two numbers are multiples, the larger number is the least common multiple of these two numbers, and the smaller number is the greatest common factor of these two numbers; Because 36 9 = 4, that is, 36 and 9 are multiples, the greatest common factor of 9 and 36 is 9, and the least common multiple is 36; So the answer is: Reviews:

This question mainly examines the finding of the greatest common factor of two numbers: the two numbers are multiples, the greatest common factor is the smaller number, and the larger number is the least common multiple of the two numbers

Because 36 9 = 4, that is, 36 and 9 are multiples, the greatest common factor of 9 and jujube 36 is 9, and the smallest common multiple is 36; Stool holes.

So the answer is: