LCM of 18 and 48 is 144. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. The smallest number among all common multiples of 18 and 48 is the LCM of 18 and 48. (18, 36, 54, 72, 90, 108, 126, etc.) and (48, 96, 144, 192, etc.) are the first few multiples of 18 and 48, respectively.
What is LCM of 18 and 48?
The answer to this question is 144. The LCM of 18 and 48 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18 and 48, is the smallest positive integer 144 which is divisible by both 18 and 48 with no remainder.
Also read: Least common multiple
How to Find LCM of 18 and 48?
LCM of 18 and 48 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 48 Using Prime Factorisation Method
The prime factorisation of 18 and 48, respectively, is given by:
18 = (2 × 3 × 3) = 21 × 32 and
48 = (2 × 2 × 2 × 2 × 3) = 24 × 31
LCM (18, 48) = 144
LCM of 18 and 48 Using Division Method
We’ll divide the numbers (18, 48) by their prime factors to get the LCM of 18 and 48 using the division method (preferably common). The LCM of 18 and 48 is calculated by multiplying these divisors.
| 2 | 18 | 48 |
| 2 | 9 | 24 |
| 2 | 9 | 12 |
| 2 | 9 | 6 |
| 3 | 9 | 3 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (18, 48) = 144
LCM of 18 and 48 Using Listing the Multiples
To calculate the LCM of 18 and 48 by listing out the common multiples, list the multiples as shown below
| Multiples of 18 | Multiples of 48 |
| 18 | 48 |
| 36 | 96 |
| 54 | 144 |
| 72 | 192 |
| 90 | – |
| …… | – |
| 144 | – |
The smallest common multiple of 18 and 48 is 144.
Therefore LCM (18, 48) = 144
Related Articles
Video Lesson on Applications of LCM
LCM of 18 and 48 Solved Example
Question: The GCD and LCM of two numbers are 6 and 144 respectively. If one number is 48, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 48 × p
⇒ p = (GCD × LCM)/48
⇒ p = (6 × 144)/48
⇒ p = 18
Therefore, the other number is 18.
Frequently Asked Questions on LCM of 18 and 48
What is the LCM of 18 and 48?
List the methods used to find the LCM of 18 and 48.
If the LCM of 48 and 18 is 144, Find its GCF.
Since the LCM of 48 and 18 = 144
⇒ 144 × GCF(48, 18) = 864
Therefore, the greatest common factor (GCF) = 864/144 = 6.
Which of the following is the LCM of 18 and 48? 28, 12, 24, 144
What is the Least Perfect Square Divisible by 18 and 48?
LCM of 18 and 48 = 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair] ⇒ Least perfect square divisible by each 18 and 48 = 144 [Square root of 144 = √144 = ±12] Therefore, 144 is the required number.
Comments