LCM of 9 and 12

LCM of 9 and 12 is 36. In mathematics, the LCM of any two numbers is the value that is evenly divisible by the two values. To find the LCM of Two Numbers that is 9 and 12, you can use one of three methods: division, listing multiples, or prime factorization. The smallest number among all frequent multiples of 9 and 12 is the LCM of 9 and 12. (9, 18, 27, 36, 45, etc.) and (12, 24, 36, 48, 60, etc.) are the first few multiples of 9 and 12.

Also read: Least common multiple

What is LCM of 9 and 12?

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

LCM of 9 and 12

How to Find LCM of 9 and 12?

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

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 9 and 12 Using Prime Factorisation Method

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

9 = 3 x 3 = 3²

12 = 2 x 2 x 3 = 2² x 31

LCM (9, 12) = 36

LCM of 9 and 12 Using Division Method

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

2 9 12
2 9 6
3 9 3
3 3 1
1 1

No further division can be done.

Hence, LCM (9, 12) = 36

LCM of 9 and 12 Using Listing the Multiples

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

Multiples of 9 Multiples of 12
9 12
18 24
27 36
36 48
45 60

The smallest common multiple of 9 and 12 is 36.

LCM (9, 12) = 36

Related Articles

Video Lesson on Applications of LCM

LCM of 9 and 12 Solved Example

The product of two numbers is 12. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1

product of numbers = 12

LCM × GCD = product of numbers

Which implies LCM = Product/GCD = 12/1

Therefore, the LCM is 12.

The probable combination for the given case is LCM(3, 4) = 12.

Frequently Asked Questions on LCM of 9 and 12

Q1

What is the LCM of 9 and 12?

The LCM of 9 and 12 is 36. To find the least common multiple of 9 and 12, we need to find the multiples of 9 and 12 (multiples of 9 = 9, 18, 27, 36; multiples of 12 = 12, 24, 36, 48) and choose the smallest multiple that is exactly divisible by 9 and 12, i.e., 36.
Q2

List the methods used to find the LCM of 9 and 12.

The methods used to find the LCM of 9 and 12 are the Prime Factorization Method, Division Method and Listing multiples.
Q3

If the LCM of 12 and 9 is 36, Find its GCF.

LCM(12, 9) × GCF(12, 9) = 12 × 9
Since the LCM of 12 and 9 = 36
⇒ 36 × GCF(12, 9) = 108
Therefore, the GCF = 108/36 = 3.

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