**What Is The Least Common Factor Of 7 And 9** – As you know There are times when we have to algebraically “tweak” how a number or equation appears in order to continue our mathematical work. We can use the greatest common factor and the least common factor to do this. The greatest common factor (GCF) is the largest number that is a factor of two or more numbers. And the least common multiple (LCM) is the smallest number that is the product of two or more numbers.

To see how these ideas come in handy? Let’s look at adding fractions. before we can add fractions We need to make sure the denominators are the same when we construct equivalent fractions:

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## What Is The Least Common Factor Of 7 And 9

In this example must find the least common multiple of 3 and 6, in other words “What is the smallest number that 3 and 6 can be divisible equally?” With a little thought, we know that 6 is the least common multiple, since 6 divided by 3 is 2, and 6 divided by 6 is 1. Then the fraction (frac ) will be adjusted to the equivalent fraction (frac ). ) By multiplying the numerator and denominator by 2, you can now add two fractions with a common denominator for the final (frac) .

### What Is The Greatest Common Factor And Least Common Multiple?

In the context of adding or subtracting fractions The least common multiple is called the least common denominator.

In general, you need to find two or more numbers greater than or equal to find the least common multiple.

It is important to note that there is more than one way to find the least common multiple. One way is to list all the multiple values in the question and select the least common one, as shown here:

This shows that the least common multiple of 8, 4, and 6 is 24 because it is least divisible by 8, 4, and 6.

#### Apt1 L.c.m And H.c.f Of Numbers

Another method involves factoring each prime, remembering that a prime number is only divisible by 1 and itself.

When the specific factor is determined Divide the list of factors once. then multiply by the remainder of the factor The result is the least common multiple:

The least common multiple can be found by common (or iterative) division. This method is sometimes considered faster and more efficient than specifying multiples and finding prime factors. Example of finding the least common multiple of 3, 6, and 9 using this method:

Divide a number by a factor of three. 6 has a factor of 2. Let’s use 2. Nine and 3 are not divisible by 2. We’ll rewrite 9 and 3 here. Repeat this process until all of the numbers are reduced to 1. Then remove the factors. They all multiplied together to find the least common multiple.

### How To Find The Greatest Common Divisor Of Two Integers

We have now introduced how to find the least common multiple. We must change our thinking to find the greatest common factor of two or more numbers. We will specify values that are less than or equal to the considered amount. in other words Ask yourself: “What is the largest value that divides these two numbers?” Understanding this concept is important for dividing and factoring polynomials.

Unique factors can also be used to determine the greatest common factor. However, instead of multiplying all the prime factors as we do with the least common factor, We multiply only the prime factors that the numbers share. The resulting product is a very common factor.

The least common multiple is greater than or equal to the number considered. while the greatest common factor is equal to or less than the number considered.

There are many techniques for earning LCM and GCF. Two of the most common strategies involve entry building or using key factors.

#### Hcf And Lcm

For example, the LCM of 5 and 6 can be obtained by listing the multiples of (5) and (6) and then listing the lowest multiple shared by the two numbers.

Likewise You can find the GCF by specifying the factors of each number and specifying the greatest common factor. For example, you can find the GCF of (40) and (32) by specifying the factors of each number.

For larger numbers Listing factors or multiples specified by GCF or LCM is not possible. for large numbers Using prime factorization techniques is more efficient.

For example, when searching for LCM, start by looking for the prime factors of each number. (This can be done by constructing a factor map.) The prime factor of (20) is (2times2times5) and the prime factor of (32) is (2times2times2times2times2). Circle common factors and count only those factors.

#### Least Common Multiple

Now multiply all the factors (Don’t forget to count the multiplier circled (2)s), which becomes (2times2times5times2times2times2) which equals (160). The LCM of (20) and (32) is (160).

When searching for GCF, start with a list of the prime factors of each number. For example, the prime factor of (45) is (5times3times3) and the prime factor of (120) is (5times3times2times2times2 . ) Now simply multiply all factors shared by both numbers. In this case we multiply (5times3) which equals (15). The GCF of (45) and (120) is (15)

The key factor approach may seem like a lengthy process. But when working with large numbers Guaranteed to save time.

The first strategy involves identifying the factors of each number. Then look for the largest factor shared by both numbers. For example, if we are looking for the GCF of (36) and (45), we can list the factors of both numbers and specify the greatest common number.

### Hcf And Lcm Using Factor Trees

List the factors of each number and specify that the greatest common factor works well for small numbers. Using the prime factorization method is more efficient.

For example, when finding the GCF of (180) and (162), we start by listing the prime factors of each number. The prime factor of (180) is (2times2times3times3times5) and the prime factor of (162) is (2times3times3times3). times3) Now look for the factor shared by both numbers. In this case, both numbers will take one (2) and two (3) or (2times3times3) . The result of (2times3times3) is (18), which is GCF! This strategy is often more effective when you get a lot of GCF.

GCF stands for “Greatest Common Factor”. GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of (24) and (36) is (12). ) Because the greatest common divisor of (24) and (36) is (12), (24) and (36) have the same other factors, but (12) is the largest factor. the most

There are several techniques for finding the least common multiple. Two common methods are to list multipliers. and use a specific factor The multiplication list is the same as it sounds. Just list the multiples of each number. Then find the lowest common multiple shared by both numbers. For example, to find the lowest common multiple of (3) and (4), list the multiples:

#### Find The Greatest Common Factor(gcf)and Least Common Factor Multiple(lcm)of Each Pair Of Integers

Multiple listings are a good strategy when numbers are relatively small. When there are large numbers, such as (38) and (42), we should use prime factorization. Start by identifying the unique factors of each number. (This can be done using a factorial chart.)

Now multiply all the factors (don’t forget to count (2) only once), which becomes (2times19times3times7) which equals (798). The LCM of (38) and (42) is (798).

LCM subtraction is a useful skill to add or subtract fractions. Find the lowest common multiple to create a common denominator for both fractions. For example, the common denominator for (frac+frac) will be (35). Since (35) is the LCM of (7) and (5), the new fraction becomes (frac+frac) which equals (frac)

We see that 2 is the only common factor of 16 and 42 and therefore is the largest common factor. We can then divide both numbers by 2 to reduce the fraction to:

### Least Common Multiple

(2=2) (Note that we can also write (2times1) , but 1 is understood or implicit. and usually don’t need to write)

Remember, when calculating the LCM of two or more numbers, We will list individual factors first when all numbers are shared. Since each of our numbers has 2 as a major factor, our LCM will also have 2 as one of the major factors.

Now in 6 we’re left with a 3 and in 8 we’re left with two 2s. We multiply these to get

Notice that although 2, 6, and 8 are all factors of 48, the answer is not D because 48 is not the least common multiple.

### Prime Factorization And Division Method For Lcm And Hcf

As we saw above, 30 is the first (least) number that 3, 5, and 6 have in common in multiples. Therefore, it is the smallest number.

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