What is the least common factor of 7 and 9?

Least Common Multiple (LCM) of 7 and 9

Step 1) First we find and list the prime factors of 7 and 9 (Prime Factorization):

Prime Factors of 7: 7 Prime Factors of 9: 3, 3 Step 2) Then we look at the frequency of the prime factors as they appear in each set above. List each prime factor the greatest number of times it occurs in either sets:

3, 3, 7 Step 3) Finally, we multiply the prime numbers from Step 2 together.

3 x 3 x 7 = 63 That's it. The Least Common Multiple (LCM) of 7 and 9 is 63.

Least Common Multiple (LCM) of 7 and 10

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 7 and 9 is 63.

LCM(7,9) = 63

Least Common Multiple of 7 and 9 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 9, than apply into the LCM equation.

GCF(7,9) = 1 LCM(7,9) = ( 7 × 9) / 1 LCM(7,9) = 63 / 1

LCM(7,9) = 63

Least Common Multiple (LCM) of 7 and 9 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 9. First we will calculate the prime factors of 7 and 9.

Prime Factorization of 7

Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:

7 = 71

Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 32

Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 9.

LCM(7,9) = 71 × 32
LCM(7,9) = 63

The LCM of 7 and 9 is 63.

Steps to find LCM

1. Find the prime factorization of 7
   7 = 7
2. Find the prime factorization of 9
   9 = 3 × 3
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

   LCM = 3 × 3 × 7

4. LCM = 63

MathStep (Works offline)

Find least common multiple (LCM) of: 14 & 18 21 & 27 35 & 45 49 & 63 14 & 9 7 & 18 21 & 9 7 & 27 35 & 9 7 & 45 49 & 9 7 & 63

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

The first step to this method of finding the Least Common Multiple of 7 and 9 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.

Let’s take a look at the multiples for each of these numbers, 7 and 9:

What are the Multiples of 7?

What are the Multiples of 9?

Let’s take a look at the first 10 multiples for each of these numbers, 7 and 9:

First 10 Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

First 10 Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 7 and 9 are 63, 126, 189. Because 63 is the smallest, it is the least common multiple.

The LCM of 7 and 9 is 63.

LCM of 7 and 9 is the smallest number among all common multiples of 7 and 9. The first few multiples of 7 and 9 are (7, 14, 21, 28, 35, 42, . . . ) and (9, 18, 27, 36, 45, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 9 - by listing multiples, by division method, and by prime factorization.

What is the LCM of 7 and 9?

Answer: LCM of 7 and 9 is 63.

Explanation:

The LCM of two non-zero integers, x(7) and y(9), is the smallest positive integer m(63) that is divisible by both x(7) and y(9) without any remainder.

Methods to Find LCM of 7 and 9

Let's look at the different methods for finding the LCM of 7 and 9.

• By Prime Factorization Method
• By Listing Multiples
• By Division Method

LCM of 7 and 9 by Prime Factorization

Prime factorization of 7 and 9 is (7) = 71 and (3 × 3) = 32 respectively. LCM of 7 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 32 × 71 = 63.
Hence, the LCM of 7 and 9 by prime factorization is 63.

LCM of 7 and 9 by Listing Multiples

To calculate the LCM of 7 and 9 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, 42, . . . ) and 9 (9, 18, 27, 36, 45, . . . . )
• Step 2: The common multiples from the multiples of 7 and 9 are 63, 126, . . .
• Step 3: The smallest common multiple of 7 and 9 is 63.

∴ The least common multiple of 7 and 9 = 63.

LCM of 7 and 9 by Division Method

To calculate the LCM of 7 and 9 by the division method, we will divide the numbers(7, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 9.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 9. Write this prime number(3) on the left of the given numbers(7 and 9), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (7, 9) is a multiple of 3, divide it by 3 and write the quotient below it. Bring down any number that is not divisible by the prime number.
• Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 7 and 9 is the product of all prime numbers on the left, i.e. LCM(7, 9) by division method = 3 × 3 × 7 = 63.

☛ Also Check:

1. Example 1: The product of two numbers is 63. If their GCD is 1, what is their LCM?

   Solution:

   Given: GCD = 1 product of numbers = 63 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 63/1 Therefore, the LCM is 63.

   The probable combination for the given case is LCM(7, 9) = 63.

Show Solution >

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The LCM of 7 and 9 is 63. To find the least common multiple (LCM) of 7 and 9, we need to find the multiples of 7 and 9 (multiples of 7 = 7, 14, 21, 28 . . . . 63; multiples of 9 = 9, 18, 27, 36 . . . . 63) and choose the smallest multiple that is exactly divisible by 7 and 9, i.e., 63.

What is the Least Perfect Square Divisible by 7 and 9?

The least number divisible by 7 and 9 = LCM(7, 9)
LCM of 7 and 9 = 3 × 3 × 7 [Incomplete pair(s): 7]
⇒ Least perfect square divisible by each 7 and 9 = LCM(7, 9) × 7 = 441 [Square root of 441 = √441 = ±21]
Therefore, 441 is the required number.

Which of the following is the LCM of 7 and 9? 30, 24, 15, 63

The value of LCM of 7, 9 is the smallest common multiple of 7 and 9. The number satisfying the given condition is 63.

If the LCM of 9 and 7 is 63, Find its GCF.

LCM(9, 7) × GCF(9, 7) = 9 × 7 Since the LCM of 9 and 7 = 63 ⇒ 63 × GCF(9, 7) = 63

Therefore, the GCF (greatest common factor) = 63/63 = 1.

How to Find the LCM of 7 and 9 by Prime Factorization?

To find the LCM of 7 and 9 using prime factorization, we will find the prime factors, (7 = 7) and (9 = 3 × 3). LCM of 7 and 9 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 9.
⇒ LCM of 7, 9 = 32 × 71 = 63.