LCM of 4, 9 and 12

LCM of 4, 9 and 12 is 36. The value evenly divisible by 4, 9 and 12 is the LCM. The least common multiple of 4, 9 and 12 can be calculated with the help of the common multiples. The multiples of 4 are (4, 8, 12, 16, 20, 24, ….), the multiples of 9 are (9, 18, 27, 36, 45, …..) and the multiples of 12 are (12, 24, 36, 48, 60, ….) respectively. Prime factorisation, listing of the multiples and division are the most commonly used methods to find the LCM

Also read: Least common multiple

What is LCM of 4, 9 and 12?

The answer to this question is 36. The LCM of 4, 9 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4, 9 and 12, is the smallest positive integer 36 which is divisible by both 4, 9 and 12 with no remainder.

lcm of 4 9 and 12

How to Find LCM of 4, 9 and 12?

LCM of 4, 9 and 12 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 4, 9 and 12 Using Prime Factorisation Method

The prime factorisation of 4, 9 and 12, respectively, is given by:

4 = 2 x 2 = 2² 

9 = 3 x 3 = 3²

12 = 2 x 2 x 3 = 2² x 3¹

LCM (4, 9, 12) = 36

LCM of 4, 9 and 12 Using Division Method

We’ll divide the numbers (4, 9, 12) by their prime factors to get the LCM of 4, 9 and 12 using the division method (preferably common). The LCM of 4, 9 and 12 is calculated by multiplying these divisors.

2

4

9

12

2

2

9

6

3

1

9

3

3

1

3

1

x

1

1

1

No further division can be done. 

Hence, LCM (4, 9, 12) = 36

LCM of 4, 9 and 12 Using Listing the Multiples

To calculate the LCM of 4, 9 and 12 by listing out the common multiples, list the multiples as shown below

Multiples of 4

Multiples of 9

Multiples of 12

4

9

12

8

18

24

12

27

36

16

36

48

20

45

60

24

54

72

28

63

84

32

72

96

36

81

108

40

90

120

LCM (4, 9, 12) = 36

Related Articles

Video Lesson on Applications of LCM

LCM of 4, 9 and 12 Solved Examples 

Question: Calculate the smallest number which is exactly divisible by 4, 9 and 12.

Solution:

The smallest number divisible by 4, 9 and 12 exactly is the LCM

(4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ….) are the multiples of 4

(9, 18, 27, 36, 45, 54, 63, ….) are the multiples of 9

(12, 24, 36, 48, 60, …..) are the multiples of 12

Hence, LCM of 4, 9 and 12 is 36.

Frequently Asked Questions on LCM of 4, 9 and 12

Q1

What is the LCM of 4, 9 and 12?

The LCM of 4, 9 and 12 is 36.
Q2

What is the GCF if the LCM of 4, 9 and 12 is 36?

LCM x GCF = 4 x 9 x 12

Given,

LCM of 4, 9 and 12 is 36

36 x GCF = 432

GCF = 432/36 = 12

Q3

What are the methods which can be applied to find the LCM of 4, 9 and 12?

The methods which can be applied to find the LCM of 4, 9 and 12 are Prime Factorisation, Division method and Listing the multiples.
Q4

The product of three numbers is 432 and the GCD is 12. Find the LCM.

Given

Product of two numbers = 432

GCD = 12

LCM x GCD = Product of two numbers

LCM = Product/GCD

LCM = 432/12 = 36

Therefore, the LCM is 36.

Q5

Using prime factorisation, find the LCM of 4, 9 and 12.

Using prime factorisation

4 = 2 x 2

9 = 3 x 3

12 = 2 x 2 x 3

LCM of 4, 9 and 12 is 36.

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