LCM of 12 and 16

LCM of 12 and 16 is 48. A way of finding the smallest common multiple between any two numbers or more is known as Least Common Multiple (LCM). The numbers (12, 24, 36, 48, 60, 72…) and (16, 32, 48, 64, 80, 96, 112….) are the first few multiples of 12 and 16, respectively. Refer to Least Common Multiple (LCM) to learn more about LCM in a descriptive manner. Let us learn how to determine the least common multiple of 12 and 16 using a simple method in this article. 

What is LCM of 12 and 16?

The answer to this question is 48. 

LCM of 12 and 16

How to Find LCM of 12 and 16?

LCM of 12 and 16 can be determined by the following three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 12 and 16 Using Prime Factorisation Method

The LCM of 12 and 16 by prime factorisation method can be determined by multiplying prime factors raised to their respective highest power.

12 = 2 × 2 × 3

16 = 2 × 2 × 2 × 2

LCM (12, 16) = 2 × 2 × 2 × 2 × 3 = 48

LCM of 12 and 16 Using Division Method

In this method, we need to divide the numbers 12 and 16 by their prime factors. The multiplication of these divisors represents the least common multiple of 12 and 16.

2

12

16

2

6

8

2

3

4

2

3

2

3

3

1

x

1

1

No more further division can be done. 

Hence, LCM (12, 16) = 2 × 2 × 2 × 2 × 3 = 48

LCM of 12 and 16 Using Listing the Multiples

In this method, we list out the multiples of 12 and 16 as shown in the below table to calculate their lowest common multiple.

Multiples of 12

Multiples of 16

12

16

24

32

36

48

48

64

60

80

LCM (12, 16) = 48

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Solved Examples

Q. 1: Find the LCM of 12 and 16 by prime factorisation method.

Solution: We can find the LCM of 12 and 16 using prime factorisation as below:

12 = 2 × 2 × 3

16 = 2 × 2 × 2 × 2 

LCM of (12, 16) = 2 × 2 × 2 × 2 × 3 = 48

Therefore the LCM of 12 and 16 is 48.

Q. 2: What is the LCM if the product of two numbers is 192 and their GCD is 4?

Solution: Given 

Product of two numbers = 192

GCD = 4

We know that

LCM × GCD = Product of two numbers

LCM = Product of two numbers/GCD

LCM = 192/4

LCM = 48

Hence the LCM is 48.

Frequently Asked Questions on LCM of 12 and 16

Q1

What is the LCM of 12 and 16?

The LCM of 12 and 16 is 48.
Q2

Mention the first five multiples of 12 and 16.

The first five multiples of 12 and 16 are as follows:

Multiples of 12 = 12, 24,36, 48, 60

Multiples of 16 = 16, 32, 48, 64, 80

Q3

Is 48 the LCM of 12 and 16?

Yes. The LCM of 12 and 16 is 48.

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