LCM of 12 and 27 - How to Find LCM of 12, 27? (2024)

LCM of 12 and 27 is the smallest number among all common multiples of 12 and 27. The first few multiples of 12 and 27 are (12, 24, 36, 48, . . . ) and (27, 54, 81, 108, 135, 162, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 27 - by listing multiples, by division method, and by prime factorization.

What is the LCM of 12 and 27?

Answer: LCM of 12 and 27 is 108.

Explanation:

The LCM of two non-zero integers, x(12) and y(27), is the smallest positive integer m(108) that is divisible by both x(12) and y(27) without any remainder.

Methods to Find LCM of 12 and 27

Let's look at the different methods for finding the LCM of 12 and 27.

• By Prime Factorization Method
• By Division Method
• By Listing Multiples

LCM of 12 and 27 by Prime Factorization

Prime factorization of 12 and 27 is (2 × 2 × 3) = 2² × 3¹ and (3 × 3 × 3) = 3³ respectively. LCM of 12 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3³ = 108.
Hence, the LCM of 12 and 27 by prime factorization is 108.

LCM of 12 and 27 by Division Method

To calculate the LCM of 12 and 27 by the division method, we will divide the numbers(12, 27) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 27.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 27. Write this prime number(2) on the left of the given numbers(12 and 27), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 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 12 and 27 is the product of all prime numbers on the left, i.e. LCM(12, 27) by division method = 2 × 2 × 3 × 3 × 3 = 108.

LCM of 12 and 27 by Listing Multiples

To calculate the LCM of 12 and 27 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 12 (12, 24, 36, 48, . . . ) and 27 (27, 54, 81, 108, 135, 162, . . . . )
• Step 2: The common multiples from the multiples of 12 and 27 are 108, 216, . . .
• Step 3: The smallest common multiple of 12 and 27 is 108.

∴ The least common multiple of 12 and 27 = 108.

☛ Also Check:

• LCM of 15, 30 and 90 - 90
• LCM of 2, 4, 6, 8, 10 and 12 - 120
• LCM of 20, 30 and 40 - 120
• LCM of 7, 8, 14 and 21 - 168
• LCM of 8 and 18 - 72
• LCM of 4 and 20 - 20
• LCM of 3 and 12 - 12

FAQs on LCM of 12 and 27

What is the LCM of 12 and 27?

The LCM of 12 and 27 is 108. To find the least common multiple (LCM) of 12 and 27, we need to find the multiples of 12 and 27 (multiples of 12 = 12, 24, 36, 48 . . . . 108; multiples of 27 = 27, 54, 81, 108) and choose the smallest multiple that is exactly divisible by 12 and 27, i.e., 108.

If the LCM of 27 and 12 is 108, Find its GCF.

LCM(27, 12) × GCF(27, 12) = 27 × 12
Since the LCM of 27 and 12 = 108
⇒ 108 × GCF(27, 12) = 324
Therefore, the greatest common factor = 324/108 = 3.

What is the Relation Between GCF and LCM of 12, 27?

The following equation can be used to express the relation between GCF and LCM of 12 and 27, i.e. GCF × LCM = 12 × 27.

What is the Least Perfect Square Divisible by 12 and 27?

The least number divisible by 12 and 27 = LCM(12, 27)
LCM of 12 and 27 = 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 12 and 27 = LCM(12, 27) × 3 = 324 [Square root of 324 = √324 = ±18]
Therefore, 324 is the required number.

What are the Methods to Find LCM of 12 and 27?

The commonly used methods to find the LCM of 12 and 27 are:

• Listing Multiples
• Prime Factorization Method
• Division Method