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LCM of 18, 36, and 27

LCM of 18, 36, and 27 is the smallest number among all common multiples of 18, 36, and 27. The first few multiples of 18, 36, and 27 are (18, 36, 54, 72, 90 . . .), (36, 72, 108, 144, 180 . . .), and (27, 54, 81, 108, 135 . . .) respectively. There are 3 commonly used methods to find LCM of 18, 36, 27 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 18, 36, and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 18, 36, and 27?

Answer: LCM of 18, 36, and 27 is 108.

Explanation:

The LCM of three non-zero integers, a(18), b(36), and c(27), is the smallest positive integer m(108) that is divisible by a(18), b(36), and c(27) without any remainder.

Methods to Find LCM of 18, 36, and 27

The methods to find the LCM of 18, 36, and 27 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 18, 36, and 27 by Division Method

To calculate the LCM of 18, 36, and 27 by the division method, we will divide the numbers(18, 36, 27) by their prime factors (preferably common). The product of these divisors gives the LCM of 18, 36, and 27.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18, 36, and 27. Write this prime number(2) on the left of the given numbers(18, 36, and 27), separated as per the ladder arrangement.
Step 2: If any of the given numbers (18, 36, 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 18, 36, and 27 is the product of all prime numbers on the left, i.e. LCM(18, 36, 27) by division method = 2 × 2 × 3 × 3 × 3 = 108.

LCM of 18, 36, and 27 by Prime Factorization

Prime factorization of 18, 36, and 27 is (2 × 3 × 3) = 2¹ × 3², (2 × 2 × 3 × 3) = 2² × 3², and (3 × 3 × 3) = 3³ respectively. LCM of 18, 36, and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3³ = 108.
Hence, the LCM of 18, 36, and 27 by prime factorization is 108.

LCM of 18, 36, and 27 by Listing Multiples

To calculate the LCM of 18, 36, 27 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 18 (18, 36, 54, 72, 90 . . .), 36 (36, 72, 108, 144, 180 . . .), and 27 (27, 54, 81, 108, 135 . . .).
Step 2: The common multiples from the multiples of 18, 36, and 27 are 108, 216, . . .
Step 3: The smallest common multiple of 18, 36, and 27 is 108.

∴ The least common multiple of 18, 36, and 27 = 108.

☛ Also Check:

LCM of 18, 36, and 27 Examples

Example 1: Calculate the LCM of 18, 36, and 27 using the GCD of the given numbers.

Solution:

Prime factorization of 18, 36, 27:
- 18 = 2¹ × 3²
- 36 = 2² × 3²
- 27 = 3³
Therefore, GCD(18, 36) = 18, GCD(36, 27) = 9, GCD(18, 27) = 9, GCD(18, 36, 27) = 9
We know,
LCM(18, 36, 27) = [(18 × 36 × 27) × GCD(18, 36, 27)]/[GCD(18, 36) × GCD(36, 27) × GCD(18, 27)]
LCM(18, 36, 27) = (17496 × 9)/(18 × 9 × 9) = 108
⇒LCM(18, 36, 27) = 108
Example 2: Find the smallest number that is divisible by 18, 36, 27 exactly.

Solution:

The smallest number that is divisible by 18, 36, and 27 exactly is their LCM.
⇒ Multiples of 18, 36, and 27:
- Multiples of 18 = 18, 36, 54, 72, 90, 108, . . . .
- Multiples of 36 = 36, 72, 108, 144, 180, . . . .
- Multiples of 27 = 27, 54, 81, 108, 135, . . . .
Therefore, the LCM of 18, 36, and 27 is 108.
Example 3: Verify the relationship between the GCD and LCM of 18, 36, and 27.

Solution:

The relation between GCD and LCM of 18, 36, and 27 is given as,
LCM(18, 36, 27) = [(18 × 36 × 27) × GCD(18, 36, 27)]/[GCD(18, 36) × GCD(36, 27) × GCD(18, 27)]
⇒ Prime factorization of 18, 36 and 27:
- 18 = 2¹ × 3²
- 36 = 2² × 3²
- 27 = 3³
∴ GCD of (18, 36), (36, 27), (18, 27) and (18, 36, 27) = 18, 9, 9 and 9 respectively.
Now, LHS = LCM(18, 36, 27) = 108.
And, RHS = [(18 × 36 × 27) × GCD(18, 36, 27)]/[GCD(18, 36) × GCD(36, 27) × GCD(18, 27)] = [(17496) × 9]/[18 × 9 × 9] = 108
LHS = RHS = 108.
Hence verified.

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FAQs on LCM of 18, 36, and 27

What is the LCM of 18, 36, and 27?

The LCM of 18, 36, and 27 is 108. To find the LCM of 18, 36, and 27, we need to find the multiples of 18, 36, and 27 (multiples of 18 = 18, 36, 54, 72, 108 . . . .; multiples of 36 = 36, 72, 108, 144 . . . .; multiples of 27 = 27, 54, 81, 108 . . . .) and choose the smallest multiple that is exactly divisible by 18, 36, and 27, i.e., 108.

What is the Least Perfect Square Divisible by 18, 36, and 27?

The least number divisible by 18, 36, and 27 = LCM(18, 36, 27)
LCM of 18, 36, and 27 = 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 18, 36, and 27 = LCM(18, 36, 27) × 3 = 324 [Square root of 324 = √324 = ±18]
Therefore, 324 is the required number.

What is the Relation Between GCF and LCM of 18, 36, 27?

The following equation can be used to express the relation between GCF and LCM of 18, 36, 27, i.e. LCM(18, 36, 27) = [(18 × 36 × 27) × GCF(18, 36, 27)]/[GCF(18, 36) × GCF(36, 27) × GCF(18, 27)].

Which of the following is the LCM of 18, 36, and 27? 3, 2, 25, 108

The value of LCM of 18, 36, 27 is the smallest common multiple of 18, 36, and 27. The number satisfying the given condition is 108.

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