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LCM of 9 and 11

LCM of 9 and 11 is the smallest number among all common multiples of 9 and 11. The first few multiples of 9 and 11 are (9, 18, 27, 36, 45, 54, . . . ) and (11, 22, 33, 44, 55, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 11 - by prime factorization, by division method, and by listing multiples.

1.	LCM of 9 and 11
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 9 and 11?

Answer: LCM of 9 and 11 is 99.

Explanation:

The LCM of two non-zero integers, x(9) and y(11), is the smallest positive integer m(99) that is divisible by both x(9) and y(11) without any remainder.

Methods to Find LCM of 9 and 11

The methods to find the LCM of 9 and 11 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 9 and 11 by Division Method

To calculate the LCM of 9 and 11 by the division method, we will divide the numbers(9, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 11.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 11. Write this prime number(3) on the left of the given numbers(9 and 11), separated as per the ladder arrangement.
Step 2: If any of the given numbers (9, 11) 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 9 and 11 is the product of all prime numbers on the left, i.e. LCM(9, 11) by division method = 3 × 3 × 11 = 99.

LCM of 9 and 11 by Prime Factorization

Prime factorization of 9 and 11 is (3 × 3) = 3² and (11) = 11¹ respectively. LCM of 9 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 11¹ = 99.
Hence, the LCM of 9 and 11 by prime factorization is 99.

LCM of 9 and 11 by Listing Multiples

To calculate the LCM of 9 and 11 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, . . . ) and 11 (11, 22, 33, 44, 55, . . . . )
Step 2: The common multiples from the multiples of 9 and 11 are 99, 198, . . .
Step 3: The smallest common multiple of 9 and 11 is 99.

∴ The least common multiple of 9 and 11 = 99.

☛ Also Check:

LCM of 9 and 11 Examples

Example 1: The GCD and LCM of two numbers are 1 and 99 respectively. If one number is 11, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 11 × b
⇒ b = (GCD × LCM)/11
⇒ b = (1 × 99)/11
⇒ b = 9
Therefore, the other number is 9.
Example 2: Verify the relationship between GCF and LCM of 9 and 11.

Solution:

The relation between GCF and LCM of 9 and 11 is given as,
LCM(9, 11) × GCF(9, 11) = Product of 9, 11
Prime factorization of 9 and 11 is given as, 9 = (3 × 3) = 3² and 11 = (11) = 11¹
LCM(9, 11) = 99
GCF(9, 11) = 1
LHS = LCM(9, 11) × GCF(9, 11) = 99 × 1 = 99
RHS = Product of 9, 11 = 9 × 11 = 99
⇒ LHS = RHS = 99
Hence, verified.
Example 3: The product of two numbers is 99. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 99
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 99/1
Therefore, the LCM is 99.
The probable combination for the given case is LCM(9, 11) = 99.

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FAQs on LCM of 9 and 11

What is the LCM of 9 and 11?

The LCM of 9 and 11 is 99. To find the least common multiple of 9 and 11, we need to find the multiples of 9 and 11 (multiples of 9 = 9, 18, 27, 36 . . . . 99; multiples of 11 = 11, 22, 33, 44 . . . . 99) and choose the smallest multiple that is exactly divisible by 9 and 11, i.e., 99.

Which of the following is the LCM of 9 and 11? 99, 5, 18, 20

The value of LCM of 9, 11 is the smallest common multiple of 9 and 11. The number satisfying the given condition is 99.

If the LCM of 11 and 9 is 99, Find its GCF.

LCM(11, 9) × GCF(11, 9) = 11 × 9
Since the LCM of 11 and 9 = 99
⇒ 99 × GCF(11, 9) = 99
Therefore, the GCF = 99/99 = 1.

What are the Methods to Find LCM of 9 and 11?

The commonly used methods to find the LCM of 9 and 11 are:

Division Method
Prime Factorization Method
Listing Multiples

How to Find the LCM of 9 and 11 by Prime Factorization?

To find the LCM of 9 and 11 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (11 = 11). LCM of 9 and 11 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 11.
⇒ LCM of 9, 11 = 3² × 11¹ = 99.

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