LCM of 120 and 180 is 360. 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 180 is the LCM of 120 and 180. (120, 240, 360, 480, 600, etc.) and (180, 360, 540, 720, 900, 1080, 1260, etc.) are the first few multiples of 120 and 180, respectively. To find the LCM of 120 and 180, there are three main methods: division, prime factorization, and listing multiples.
Also read: Least common multiple
What is LCM of 120 and 180?
The answer to this question is 360. The LCM of 120 and 180 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 120 and 180, is the smallest positive integer 360 which is divisible by both 120 and 180 with no remainder.
How to Find LCM of 120 and 180?
LCM of 120 and 180 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 120 and 180 Using Prime Factorisation Method
The prime factorisation of 120 and 180, respectively, is given by:
120 = (2 × 2 × 2 × 3 × 5) = 23 × 31 × 51 and
180 = (2 × 2 × 3 × 3 × 5) = 22 × 32 × 51
LCM (120, 180) = 360
LCM of 120 and 180 Using Division Method
We’ll divide the numbers (120, 180) by their prime factors to get the LCM of 120 and 180 using the division method (preferably common). The LCM of 120 and 180 is calculated by multiplying these divisors.
| 2 | 120 | 180 |
| 2 | 60 | 90 |
| 2 | 30 | 45 |
| 3 | 15 | 45 |
| 3 | 5 | 15 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (120, 180) = 360
LCM of 120 and 180 Using Listing the Multiples
To calculate the LCM of 120 and 180 by listing out the common multiples, list the multiples as shown below
| Multiples of 120 | Multiples of 180 |
| 120 | 180 |
| 240 | 360 |
| 360 | 540 |
| 480 | 720 |
| 600 | 900 |
The smallest common multiple of 120 and 180 is 360.
Therefore LCM (120, 180) = 360
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LCM of 120 and 180 Solved Example
Question: The GCD and LCM of two numbers are 60 and 360 respectively. If one number is 180, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 180 × a
⇒ a = (GCD × LCM)/180
⇒ a = (60 × 360)/180
⇒ a = 120
Therefore, the other number is 120.
Frequently Asked Questions on LCM of 120 and 180
What is the LCM of 120 and 180?
List the methods used to find the LCM of 120 and 180.
If the LCM of 180 and 120 is 360, Find its GCF.
Since the LCM of 180 and 120 = 360
⇒ 360 × GCF(180, 120) = 21600
Therefore, the GCF = 21600/360 = 60.
Which of the following is the LCM of 120 and 180? 360, 40, 10, 42
How to Find the LCM of 120 and 180 by Prime Factorization?
⇒ LCM of 120, 180 = 360.
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