LCM of 6, 12 and 18

LCM of 6, 12 and 18 is 36. The number which evenly divides 6, 12 and 18 gives the value of LCM. The common multiples of the two numbers will provide the least common multiple of 6, 12 and 18. The multiples of 6 are (6, 12, 18, 24, 30, 36, ….), the multiples of 12 are (12, 24, 36, 48, 60, …..) and the multiples of 18 are (18, 36, 54, 72, 90, …..) respectively. For a clear-cut knowledge of the LCM concept and methods like prime factorisation, division and listing out the multiples, make use of the reference materials at BYJU’S. 

Also read: Least common multiple

What is LCM of 6, 12 and 18?

The answer to this question is 36. The LCM of 6, 12 and 18 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6, 12 and 18, is the smallest positive integer 36 which is divisible by both 6, 12 and 18 with no remainder.

LCM of 6 12 and 18

How to Find LCM of 6, 12 and 18?

LCM of 6, 12 and 18 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 6, 12 and 18 Using Prime Factorisation Method

The prime factorisation of 6, 12 and 18, respectively, is given by:

6 = 2 x 3 = 2¹ x 3¹

12 = 2 x 2 x 3 = 2² x 3¹

18 = 2 x 3 x 3 = 2¹ x 3²

LCM (6, 12, 18) = 36

LCM of 6, 12 and 18 Using Division Method

We’ll divide the numbers (6, 12, 18) by their prime factors to get the LCM of 6, 12 and 18 using the division method (preferably common). The LCM of 6, 12 and 18 is calculated by multiplying these divisors.

2

6

12

18

2

3

6

9

3

3

3

9

3

1

1

3

x

1

1

1

No further division can be done. 

Hence, LCM (6, 12, 18) = 36

LCM of 6, 12 and 18 Using Listing the Multiples

To calculate the LCM of 6, 12 and 18 by listing out the common multiples, list the multiples as shown below.

Multiples of 6

Multiples of 12

Multiples of 18

6

12

18

12

24

36

18

36

54

24

48

72

30

60

90

36

72

108

42

84

126

LCM (6, 12, 18) = 36

Related Articles

Video Lesson on Applications of LCM

LCM of 6, 12 and 18 Solved Examples 

Question: Determine the smallest number divisible by 6, 12 and 18 exactly.

Solution:

The smallest number divisible by 6, 12 and 18 exactly is LCM.

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, ….

Multiples of 12 = 12, 24, 36, 48, 60, 72, ….

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

Therefore, the LCM of 6, 12 and 18 is 36.

Frequently Asked Questions on LCM of 6, 12 and 18

Q1

Find the GCF if the LCM of 6, 12 and 18 is 36.

We know that,

LCM x GCF = 6 x 12 x 18

As LCM (6, 12, 18) is 36

36 x GCF = 1296

GCF = 1296/36 = 36

Q2

Find the LCM of 6, 12 and 18.

First the multiples of 6, 12 and 18 have to be found to get the LCM value. The smallest multiple exactly divisible by 6, 12 and 18 is 36.
Q3

Show the relation between GCF and LCM of 6, 12 and 18.

The relation between GCF and LCM of 6, 12 and 18 is

LCM x GCF = 6 x 12 x 18

LCM x GCF = 1296

Q4

What is the LCM of 6, 12 and 18?

The LCM of 6, 12 and 18 is 36.
Q5

In 45, 30, 36 and 20, find the LCM of 6, 12 and 18.

The LCM value is the smallest common multiple which is divisible evenly by 6, 12 and 18. The number which satisfies this condition is 36.

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