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LCM of 54 and 27

LCM of 54 and 27 is the smallest number among all common multiples of 54 and 27. The first few multiples of 54 and 27 are (54, 108, 162, 216, 270, . . . ) and (27, 54, 81, 108, 135, 162, 189, . . . ) respectively. There are 3 commonly used methods to find LCM of 54 and 27 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 54 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 54 and 27?

Answer: LCM of 54 and 27 is 54.

Explanation:

The LCM of two non-zero integers, x(54) and y(27), is the smallest positive integer m(54) that is divisible by both x(54) and y(27) without any remainder.

Methods to Find LCM of 54 and 27

The methods to find the LCM of 54 and 27 are explained below.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 54 and 27 by Division Method

To calculate the LCM of 54 and 27 by the division method, we will divide the numbers(54, 27) by their prime factors (preferably common). The product of these divisors gives the LCM of 54 and 27.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 54 and 27. Write this prime number(2) on the left of the given numbers(54 and 27), separated as per the ladder arrangement.
Step 2: If any of the given numbers (54, 27) is a multiple of 2, divide it by 2 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 54 and 27 is the product of all prime numbers on the left, i.e. LCM(54, 27) by division method = 2 × 3 × 3 × 3 = 54.

LCM of 54 and 27 by Listing Multiples

To calculate the LCM of 54 and 27 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 54 (54, 108, 162, 216, 270, . . . ) and 27 (27, 54, 81, 108, 135, 162, 189, . . . . )
Step 2: The common multiples from the multiples of 54 and 27 are 54, 108, . . .
Step 3: The smallest common multiple of 54 and 27 is 54.

∴ The least common multiple of 54 and 27 = 54.

LCM of 54 and 27 by Prime Factorization

Prime factorization of 54 and 27 is (2 × 3 × 3 × 3) = 2¹ × 3³ and (3 × 3 × 3) = 3³ respectively. LCM of 54 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3³ = 54.
Hence, the LCM of 54 and 27 by prime factorization is 54.

☛ Also Check:

LCM of 54 and 27 Examples

Example 1: The product of two numbers is 1458. If their GCD is 27, what is their LCM?

Solution:

Given: GCD = 27
product of numbers = 1458
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1458/27
Therefore, the LCM is 54.
The probable combination for the given case is LCM(54, 27) = 54.
Example 2: Find the smallest number that is divisible by 54 and 27 exactly.

Solution:

The smallest number that is divisible by 54 and 27 exactly is their LCM.
⇒ Multiples of 54 and 27:
- Multiples of 54 = 54, 108, 162, 216, 270, 324, . . . .
- Multiples of 27 = 27, 54, 81, 108, 135, 162, . . . .
Therefore, the LCM of 54 and 27 is 54.
Example 3: Verify the relationship between GCF and LCM of 54 and 27.

Solution:

The relation between GCF and LCM of 54 and 27 is given as,
LCM(54, 27) × GCF(54, 27) = Product of 54, 27
Prime factorization of 54 and 27 is given as, 54 = (2 × 3 × 3 × 3) = 2¹ × 3³ and 27 = (3 × 3 × 3) = 3³
LCM(54, 27) = 54
GCF(54, 27) = 27
LHS = LCM(54, 27) × GCF(54, 27) = 54 × 27 = 1458
RHS = Product of 54, 27 = 54 × 27 = 1458
⇒ LHS = RHS = 1458
Hence, verified.

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FAQs on LCM of 54 and 27

What is the LCM of 54 and 27?

The LCM of 54 and 27 is 54. To find the LCM (least common multiple) of 54 and 27, we need to find the multiples of 54 and 27 (multiples of 54 = 54, 108, 162, 216; multiples of 27 = 27, 54, 81, 108) and choose the smallest multiple that is exactly divisible by 54 and 27, i.e., 54.

How to Find the LCM of 54 and 27 by Prime Factorization?

To find the LCM of 54 and 27 using prime factorization, we will find the prime factors, (54 = 2 × 3 × 3 × 3) and (27 = 3 × 3 × 3). LCM of 54 and 27 is the product of prime factors raised to their respective highest exponent among the numbers 54 and 27.
⇒ LCM of 54, 27 = 2¹ × 3³ = 54.

If the LCM of 27 and 54 is 54, Find its GCF.

LCM(27, 54) × GCF(27, 54) = 27 × 54
Since the LCM of 27 and 54 = 54
⇒ 54 × GCF(27, 54) = 1458
Therefore, the GCF = 1458/54 = 27.

What is the Relation Between GCF and LCM of 54, 27?

The following equation can be used to express the relation between GCF and LCM of 54 and 27, i.e. GCF × LCM = 54 × 27.

Which of the following is the LCM of 54 and 27? 54, 12, 40, 18

The value of LCM of 54, 27 is the smallest common multiple of 54 and 27. The number satisfying the given condition is 54.

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