LCM of 120 and 144 is 720. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 120 and 144 is the LCM of 120 and 144. (120, 240, 360, 480, etc.) and (144, 288, 432, 576, 720, etc.) are the first few multiples of 120 and 144, respectively. To find the LCM of 120 and 144, there are three main methods: division, prime factorization, and listing multiples.
Also read: Least common multiple
What is LCM of 120 and 144?
The answer to this question is 720. The LCM of 120 and 144 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 120 and 144, is the smallest positive integer 720 which is divisible by both 120 and 144 with no remainder.
How to Find LCM of 120 and 144?
LCM of 120 and 144 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 120 and 144 Using Prime Factorisation Method
The prime factorisation of 120 and 144, respectively, is given by:
120 = (2 × 2 × 2 × 3 × 5) = 23 × 31 × 51 and
144 = (2 × 2 × 2 × 2 × 3 × 3) = 24 × 32
LCM (120, 144) = 720
LCM of 120 and 144 Using Division Method
We’ll divide the numbers (120, 144) by their prime factors to get the LCM of 120 and 144 using the division method (preferably common). The LCM of 120 and 144 is calculated by multiplying these divisors.
| 2 | 120 | 144 |
| 2 | 60 | 72 |
| 2 | 30 | 36 |
| 2 | 15 | 18 |
| 3 | 15 | 9 |
| 3 | 5 | 3 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (120, 144) = 720.
LCM of 120 and 144 Using Listing the Multiples
To calculate the LCM of 120 and 144 by listing out the common multiples, list the multiples as shown below
| Multiples of 120 | Multiples of 144 |
| 120 | 144 |
| 240 | 288 |
| 360 | 432 |
| 480 | 576 |
| 600 | 720 |
| 720 | – |
The smallest common multiple of 120 and 144 is 720.
Therefore LCM (120, 144) = 720
Related Articles
Video Lesson on Applications of LCM
LCM of 120 and 144 Solved Example
Question: The product of two numbers is 17280. If their GCD is 24, what is their LCM?
Solution:
Given: GCD = 24
product of numbers = 17280
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 17280/24
Therefore, the LCM is 720.
The probable combination for the given case is LCM(120, 144) = 720.
Frequently Asked Questions on LCM of 120 and 144
What is the LCM of 120 and 144?
List the methods used to find the LCM of 120 and 144.
If the LCM of 144 and 120 is 720, Find its GCF.
Since the LCM of 144 and 120 = 720
⇒ 720 × GCF(144, 120) = 17280
Therefore, the GCF = 17280/720 = 24.
Which of the following is the LCM of 120 and 144? 24, 30, 720, 10
How to Find the LCM of 120 and 144 by Prime Factorization?
⇒ LCM of 120, 144 = 720.
Comments