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LCM of 27 and 36

LCM of 27 and 36 is the smallest number among all common multiples of 27 and 36. The first few multiples of 27 and 36 are (27, 54, 81, 108, 135, 162, 189, . . . ) and (36, 72, 108, 144, 180, 216, 252, . . . ) respectively. There are 3 commonly used methods to find LCM of 27 and 36 - by prime factorization, by division method, and by listing multiples.

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

What is the LCM of 27 and 36?

Answer: LCM of 27 and 36 is 108.

Explanation:

The LCM of two non-zero integers, x(27) and y(36), is the smallest positive integer m(108) that is divisible by both x(27) and y(36) without any remainder.

Methods to Find LCM of 27 and 36

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

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 27 and 36 by Listing Multiples

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

Step 1: List a few multiples of 27 (27, 54, 81, 108, 135, 162, 189, . . . ) and 36 (36, 72, 108, 144, 180, 216, 252, . . . . )
Step 2: The common multiples from the multiples of 27 and 36 are 108, 216, . . .
Step 3: The smallest common multiple of 27 and 36 is 108.

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

LCM of 27 and 36 by Division Method

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

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

LCM of 27 and 36 by Prime Factorization

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

☛ Also Check:

LCM of 27 and 36 Examples

Example 1: Find the smallest number that is divisible by 27 and 36 exactly.

Solution:

The smallest number that is divisible by 27 and 36 exactly is their LCM.
⇒ Multiples of 27 and 36:
- Multiples of 27 = 27, 54, 81, 108, 135, 162, 189, . . . .
- Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, . . . .
Therefore, the LCM of 27 and 36 is 108.
Example 2: Verify the relationship between GCF and LCM of 27 and 36.

Solution:

The relation between GCF and LCM of 27 and 36 is given as,
LCM(27, 36) × GCF(27, 36) = Product of 27, 36
Prime factorization of 27 and 36 is given as, 27 = (3 × 3 × 3) = 3³ and 36 = (2 × 2 × 3 × 3) = 2² × 3²
LCM(27, 36) = 108
GCF(27, 36) = 9
LHS = LCM(27, 36) × GCF(27, 36) = 108 × 9 = 972
RHS = Product of 27, 36 = 27 × 36 = 972
⇒ LHS = RHS = 972
Hence, verified.
Example 3: The GCD and LCM of two numbers are 9 and 108 respectively. If one number is 27, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 27 × m
⇒ m = (GCD × LCM)/27
⇒ m = (9 × 108)/27
⇒ m = 36
Therefore, the other number is 36.

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FAQs on LCM of 27 and 36

What is the LCM of 27 and 36?

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

Which of the following is the LCM of 27 and 36? 12, 2, 25, 108

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

How to Find the LCM of 27 and 36 by Prime Factorization?

To find the LCM of 27 and 36 using prime factorization, we will find the prime factors, (27 = 3 × 3 × 3) and (36 = 2 × 2 × 3 × 3). LCM of 27 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 27 and 36.
⇒ LCM of 27, 36 = 2² × 3³ = 108.

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

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

If the LCM of 36 and 27 is 108, Find its GCF.

LCM(36, 27) × GCF(36, 27) = 36 × 27
Since the LCM of 36 and 27 = 108
⇒ 108 × GCF(36, 27) = 972
Therefore, the greatest common factor (GCF) = 972/108 = 9.

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