LCM of 18 and 27

LCM of 18 and 27 is 54. The smallest number among all common multiples of 18 and 27 is the LCM of 18 and 27. (18, 36, 54, 72, 90, 108, 126, etc.) and (27, 54, 81, 108, 135, etc.) are the first few multiples of 18 and 27. To find the LCM of 18 and 27, there are three typical methods: listing multiples, division method, and prime factorization. The LCM of Two Numbers in mathematics is the value that is evenly divisible by the two values.

Also read: Least common multiple

What is LCM of 18 and 27?

The answer to this question is 54. The LCM of 18 and 27 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18 and 27, is the smallest positive integer 54 which is divisible by both 18 and 27 with no remainder.

lcm of 18 and 27

How to Find LCM of 18 and 27?

LCM of 18 and 27 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 18 and 27 Using Prime Factorisation Method

The prime factorisation of 18 and 27, respectively, is given by:

18 = (2 × 3 × 3) = 21 × 32

27 = (3 × 3 × 3) = 33

LCM (18, 27) = 54

LCM of 18 and 27 Using Division Method

We’ll divide the numbers (18, 27) by their prime factors to get the LCM of 18 and 27 using the division method (preferably common). The LCM of 18 and 27 is calculated by multiplying these divisors.

2 18 27
3 9 27
3 3 9
3 1 3
1 1

No further division can be done.

Hence, LCM (18, 27) = 54

LCM of 18 and 27 Using Listing the Multiples

To calculate the LCM of 18 and 27 by listing out the common multiples, list the multiples as shown below

Multiples of 18 Multiples of 27
18 27
36 54
54 81
72 108
90 135

The smallest common multiple of 18 and 27 is 54.

LCM (18, 27) = 54

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Video Lesson on Applications of LCM

LCM of 18 and 27 Solved Example

Find the smallest number that is divisible by 18 and 27 exactly.

Solution:

The smallest number that is divisible by 18 and 27 exactly is their LCM.

Multiples of 18 and 27:

Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, . . . .

Multiples of 27 = 27, 54, 81, 108, 135, 162, 189, . . . .

Therefore, the LCM of 18 and 27 is 54.

Frequently Asked Questions on LCM of 18 and 27

Q1

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.
Q2

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
Q3

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.

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