LCM of 3 9 and 12

LCM of 3, 9 and 12 is 36. LCM stands for Least Common Multiple or the Lowest Common Multiple also known as LCD Least Common Divisor is the positive number that is a common multiple to the given numbers. Here the given set of numbers are 3, 9 and 12. The smallest common multiple for all these numbers among many is 36, and hence it is the LCM. You can refer to LCM with Examples to understand better.

What is LCM of 3, 9 and 12

The Least Common Multiple or Lowest Common Multiple of 3, 9 and 12 is 36.

Lcm Of 3 9 And 12

How to Find LCM of 3, 9 and 12?

LCM of 3, 9 and 12 can be determined using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 3, 9 and 12 Using Prime Factorisation Method

In the Prime Factorisation method, the numbers 3, 9 and 12 can be expressed as;

3 = 1 × 3

9 = 3 × 3

12 = 2 × 2 × 3

3 is the common factor of 3, 9 and 12. 3 along with other prime factors of 9 and 12 are multiplied to get the LCM.

LCM(3, 9 and 12) = 2 × 2 × 3 × 3 = 36

LCM of 3, 9 and 12 Using Division Method

In the Division Method, the numbers 3, 9 and 12 are divided by common prime divisors. The product of common and other prime divisors of 3, 9 and 12 forms the LCM.

2

3

9

12

2

3

9

6

3

3

9

3

3

1

3

1

×

1

1

1

LCM(3, 9 and 12) = 2 × 2 × 3 × 3 = 36

LCM of 3, 9 and 12 Using Listing the Multiples

By listing all the multiples of 3, 9 and 12, we can identify the LCM. Below is the list of multiples for 3, 9 and 12

Multiples of 3

Multiples of 9

Multiples of 12

3

9

12

6

18

24

9

27

36

12

36

48

15

45

60

18

54

72

21

63

84

24

72

96

27

81

108

30

90

120

33

99

132

36

108

144

LCM(3, 9 and 12) = 36

Related Articles

Video Lesson on Applications of LCM

Solved Examples 

What is the smallest number that is divisible by 3, 9 and 12?

Answer: 36 is the smallest number that is divisible by 3, 9 and 12. 

What is the LCM of 3 and 36?

Answer: LCM of 3 and 36 is 36.

Frequently Asked Questions on LCM of 3, 9 and 12

What is the LCM of 3, 9 and 12?

The LCM of 3, 9 and 12 is 36.

What is the difference between the LCM 3, 9 and 12 and HCF of 3, 9 and 12?

The LCM of 3, 9 and 12 is 36 and HCF of 3, 9 and 12 is 3.

Is the LCM and LCD both the same for 3, 9 and 12?

Yes. The LCM and Lowest Common Divisor are both the same for 3, 9 and 12  which is 36.

What are the first 3 common multiples of 3, 9 and 12?

The first three common multiples of 3, 9 and 12 are 36, 72, and 108.

Is the LCM of 3 and 9 same as the LCM of 9 and 12?

No. LCM of 3 and 9 is 9, whereas the LCM of 9 and 12 is 36. They are not the same.

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