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.

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

Answer: LCM of 18 and 27 is 54.

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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 MultiplesBy Division MethodBy 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

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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 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.

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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 MultiplesDivision MethodPrime 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.

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