LCM of 18 and 27

LCM of 18 and 27 is the smallest number among all common multiples of 18 and 27. The first few multiples of 18 and 27 are (18, 36, 54, 72, 90, 108, 126, . . . ) and (27, 54, 81, 108, 135, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 27 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 18 and 27 is 54.

Explanation:

The LCM of two non-zero integers, x(18) and y(27), is the smallest positive integer m(54) that is divisible by both x(18) and y(27) without any remainder.

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

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

LCM of 18 and 27 by Listing Multiples

To calculate the LCM of 18 and 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, 108, 126, . . . ) and 27 (27, 54, 81, 108, 135, . . . . )
• Step 2: The common multiples from the multiples of 18 and 27 are 54, 108, . . .
• Step 3: The smallest common multiple of 18 and 27 is 54.

∴ The least common multiple of 18 and 27 = 54.

LCM of 18 and 27 by Division Method

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

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 27. Write this prime number(2) on the left of the given numbers(18 and 27), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (18, 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 and 27 is the product of all prime numbers on the left, i.e. LCM(18, 27) by division method = 2 × 3 × 3 × 3 = 54.

LCM of 18 and 27 by Prime Factorization

Prime factorization of 18 and 27 is (2 × 3 × 3) = 2¹ × 3² and (3 × 3 × 3) = 3³ respectively. LCM of 18 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3³ = 54.
Hence, the LCM of 18 and 27 by prime factorization is 54.

☛ Also Check:

• LCM of 35, 12 and 70 - 420
• LCM of 8, 9 and 12 - 72
• LCM of 10 and 40 - 40
• LCM of 4 and 18 - 36
• LCM of 10 and 14 - 70
• LCM of 35 and 40 - 280
• LCM of 28 and 32 - 224

FAQs on LCM of 18 and 27

What is the LCM of 18 and 27?

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

What are the Methods to Find LCM of 18 and 27?

The commonly used methods to find the LCM of 18 and 27 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

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

The following equation can be used to express the relation between GCF and LCM of 18 and 27, i.e. GCF × LCM = 18 × 27.

How to Find the LCM of 18 and 27 by Prime Factorization?

To find the LCM of 18 and 27 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (27 = 3 × 3 × 3). LCM of 18 and 27 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 27.
⇒ LCM of 18, 27 = 2¹ × 3³ = 54.

If the LCM of 27 and 18 is 54, Find its GCF.

LCM(27, 18) × GCF(27, 18) = 27 × 18
Since the LCM of 27 and 18 = 54
⇒ 54 × GCF(27, 18) = 486
Therefore, the GCF (greatest common factor) = 486/54 = 9.