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LCM of 9 and 27

LCM of 9 and 27 is the smallest number among all common multiples of 9 and 27. The first few multiples of 9 and 27 are (9, 18, 27, 36, 45, 54, . . . ) and (27, 54, 81, 108, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 27 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 9 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 9 and 27?

Answer: LCM of 9 and 27 is 27.

Explanation:

The LCM of two non-zero integers, x(9) and y(27), is the smallest positive integer m(27) that is divisible by both x(9) and y(27) without any remainder.

Methods to Find LCM of 9 and 27

The methods to find the LCM of 9 and 27 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 9 and 27 by Prime Factorization

Prime factorization of 9 and 27 is (3 × 3) = 3² and (3 × 3 × 3) = 3³ respectively. LCM of 9 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3³ = 27.
Hence, the LCM of 9 and 27 by prime factorization is 27.

LCM of 9 and 27 by Listing Multiples

To calculate the LCM of 9 and 27 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 27 (27, 54, 81, 108, . . . . )
Step 2: The common multiples from the multiples of 9 and 27 are 27, 54, . . .
Step 3: The smallest common multiple of 9 and 27 is 27.

∴ The least common multiple of 9 and 27 = 27.

LCM of 9 and 27 by Division Method

To calculate the LCM of 9 and 27 by the division method, we will divide the numbers(9, 27) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 27.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 27. Write this prime number(3) on the left of the given numbers(9 and 27), separated as per the ladder arrangement.
Step 2: If any of the given numbers (9, 27) 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 27 is the product of all prime numbers on the left, i.e. LCM(9, 27) by division method = 3 × 3 × 3 = 27.

☛ Also Check:

LCM of 9 and 27 Examples

Example 1: Verify the relationship between GCF and LCM of 9 and 27.

Solution:

The relation between GCF and LCM of 9 and 27 is given as,
LCM(9, 27) × GCF(9, 27) = Product of 9, 27
Prime factorization of 9 and 27 is given as, 9 = (3 × 3) = 3² and 27 = (3 × 3 × 3) = 3³
LCM(9, 27) = 27
GCF(9, 27) = 9
LHS = LCM(9, 27) × GCF(9, 27) = 27 × 9 = 243
RHS = Product of 9, 27 = 9 × 27 = 243
⇒ LHS = RHS = 243
Hence, verified.
Example 2: The GCD and LCM of two numbers are 9 and 27 respectively. If one number is 27, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 27 × p
⇒ p = (GCD × LCM)/27
⇒ p = (9 × 27)/27
⇒ p = 9
Therefore, the other number is 9.
Example 3: The product of two numbers is 243. If their GCD is 9, what is their LCM?

Solution:

Given: GCD = 9
product of numbers = 243
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 243/9
Therefore, the LCM is 27.
The probable combination for the given case is LCM(9, 27) = 27.

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FAQs on LCM of 9 and 27

What is the LCM of 9 and 27?

The LCM of 9 and 27 is 27. To find the LCM (least common multiple) of 9 and 27, we need to find the multiples of 9 and 27 (multiples of 9 = 9, 18, 27, 36; multiples of 27 = 27, 54, 81, 108) and choose the smallest multiple that is exactly divisible by 9 and 27, i.e., 27.

What is the Least Perfect Square Divisible by 9 and 27?

The least number divisible by 9 and 27 = LCM(9, 27)
LCM of 9 and 27 = 3 × 3 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 9 and 27 = LCM(9, 27) × 3 = 81 [Square root of 81 = √81 = ±9]
Therefore, 81 is the required number.

How to Find the LCM of 9 and 27 by Prime Factorization?

To find the LCM of 9 and 27 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (27 = 3 × 3 × 3). LCM of 9 and 27 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 27.
⇒ LCM of 9, 27 = 3³ = 27.

If the LCM of 27 and 9 is 27, Find its GCF.

LCM(27, 9) × GCF(27, 9) = 27 × 9
Since the LCM of 27 and 9 = 27
⇒ 27 × GCF(27, 9) = 243
Therefore, the greatest common factor (GCF) = 243/27 = 9.

Which of the following is the LCM of 9 and 27? 35, 27, 32, 40

The value of LCM of 9, 27 is the smallest common multiple of 9 and 27. The number satisfying the given condition is 27.

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