LCM of 3 and 12

LCM of 3 and 12 is 12. The smallest number among all common multiples of 3 and 12 is the LCM of 3 and 12. (3, 6, 9, 12, 15, 18, 21, etc.) and (12, 24, 36, 48, 60, etc.) are the first few multiples of 3 and 12. In mathematics, the LCM of Two Numbers is the value that is evenly divisible by the two values. To find the LCM of 3 and 12, there are three typical methods: prime factorization, listing multiples, and division.

What is LCM of 3 and 12?

The answer to this question is 12. The LCM of 3 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 12, is the smallest positive integer 12 which is divisible by both 3 and 12 with no remainder.

lcm of 3 and 12

Also read: Least common multiple

How to Find LCM of 3 and 12?

LCM of 3 and 12 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 3 and 12 Using Prime Factorisation Method

The prime factorisation of 3 and 12, respectively, is given by:

(3) = 31

and

12 = (2 × 2 × 3) = 22 × 31

LCM (3, 12) = 12

LCM of 3 and 12 Using Division Method

We’ll divide the numbers (3, 12) by their prime factors to get the LCM of 3 and 12 using the division method (preferably common). The LCM of 3 and 12 is calculated by multiplying these divisors.

2 3 12
2 3 6
3 3 3
x 1 1

No further division can be done.

Hence, LCM (3, 12) = 12.

LCM of 3 and 12 Using Listing the Multiples

To calculate the LCM of 3 and 12 by listing out the common multiples, list the multiples as shown below.

Multiples of 3 Multiples of 12
3 12
6 24
9 36
12 48
15 60

The smallest common multiple of 3 and 12 is 12.

LCM (3, 12) = 12

Related Articles

Video Lesson on Applications of LCM

LCM of 3 and 12 Solved Example

The product of two numbers is 36. If their GCD is 3, what is their LCM?

Given: GCD = 3

product of numbers = 36

LCM × GCD = product of numbers

LCM = Product/GCD = 36/3

Therefore, the LCM is 12.

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

Frequently Asked Questions on LCM of 3 and 12

Q1

What is the LCM of 3 and 12?

The LCM of 3 and 12 is 12. To find the least common multiple of 3 and 12, we need to find the multiples of 3 and 12 (multiples of 3 = 3, 6, 9, 12; multiples of 12 = 12, 24, 36, 48) and choose the smallest multiple that is exactly divisible by 3 and 12, i.e., 12.
Q2

List the methods used to find the LCM of 3 and 12.

The methods used to find the LCM of 3 and 12 are the Prime Factorization Method, Division Method and Listing multiples.
Q3

If the LCM of 12 and 3 is 12, Find its GCF.

LCM(12, 3) × GCF(12, 3) = 12 × 3
Since the LCM of 12 and 3 = 12
⇒ 12 × GCF(12, 3) = 36
Therefore, the greatest common factor (GCF) = 36/12 = 3.C

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