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.
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
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
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
What is the LCM of 12 and 16?
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
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