LCM of 12 and 48 is 48. The full form of LCM is the least common multiple. It is used to add or subtract any two fractions when the denominators of the fractions are not equal. The LCM concept is used to make the simplification process easier. Learn to find the LCM of numbers using prime factorisation, division method and listing multiples by following Least Common Multiple (LCM) in detail. In this article, we will learn how to determine the least common multiple of 12 and 48 in simple and understandable language.
What is LCM of 12 and 48?
The answer to this question is 48.
How to Find LCM of 12 and 48?
The below methods are used to find the LCM of 12 and 48:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 48 Using Prime Factorisation Method
By prime factorisation method, we can write 12 and 48 as the product of prime numbers, such that;
12 = 2 × 2 × 3
48 = 2 × 2 × 2 × 2 × 3
LCM (12, 48) = 2 × 2 × 2 × 2 × 3 = 48
LCM of 12 and 48 Using Division Method
To find the least common multiple of 12 and 48 using division method, we divide the numbers 12 and 48 by their prime factors. The product of these divisors denotes the least common multiple of 12 and 48.
|
2 |
12 |
48 |
|
2 |
6 |
24 |
|
2 |
3 |
12 |
|
2 |
3 |
6 |
|
3 |
3 |
3 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (12, 48) = 2 × 2 × 2 × 2 × 3 = 48
LCM of 12 and 48 Using Listing the Multiples
Here we list out the multiples of 12 and 48 to calculate their least common multiple as shown in the below table:
|
Multiples of 12 |
Multiples of 48 |
|
12 |
48 |
|
24 |
96 |
|
36 |
144 |
|
48 |
192 |
|
60 |
240 |
LCM (12, 48) = 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 48 by listing multiples.
Solution: First, list out the multiples of 12 and 48
Multiples of 12 = 12, 24, 36, 48, 60, …..
Multiples of 48 = 48, 96, 144, 192, 240,…..
Here, the smallest common multiple of 12 and 48 is 48
Therefore the least common multiple of 12 and 48 is 48.
Q. 2: The GCD and LCM of the two numbers are 12 and 48. If one number is 48, determine the other number.
Solution: Let the other number be k
We know that,
GCD × LCM = 48 × k
k = (GCD × LCM) / 48
k = (12 × 48) / 48
k = 12
Hence the other number is 12.
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