LCM of 120 and 160 is 480. 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 120 and 160 is the LCM of 120 and 160. (120, 240, 360, 480, 600, 720, etc.) and (160, 320, 480, 640, 800, 960, etc.) are the first few multiples of 120 and 160, respectively.
Also read: Least common multiple
What is LCM of 120 and 160?
The answer to this question is 480. The LCM of 120 and 160 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 120 and 160, is the smallest positive integer 480 which is divisible by both 120 and 160 with no remainder.
How to Find LCM of 120 and 160?
LCM of 120 and 160 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 120 and 160 Using Prime Factorisation Method
The prime factorisation of 120 and 160, respectively, is given by:
120 = (2 × 2 × 2 × 3 × 5) = 23 × 31 × 51 and
160 = (2 × 2 × 2 × 2 × 2 × 5) = 25 × 51
LCM (120, 160) = 72
LCM of 120 and 160 Using Division Method
We’ll divide the numbers (120, 160) by their prime factors to get the LCM of 120 and 160 using the division method (preferably common). The LCM of 120 and 160 is calculated by multiplying these divisors.
| 2 | 120 | 160 |
| 2 | 60 | 80 |
| 2 | 30 | 40 |
| 2 | 15 | 20 |
| 2 | 15 | 10 |
| 3 | 15 | 5 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (120, 160) = 480
LCM of 120 and 160 Using Listing the Multiples
To calculate the LCM of 120 and 160 by listing out the common multiples, list the multiples as shown below.
| Multiples of 120 | Multiples of 160 |
| 120 | 160 |
| 240 | 320 |
| 360 | 480 |
| 480 | 640 |
| 600 | 800 |
The smallest common multiple of 120 and 160 is 480.
Therefore LCM (120, 160) = 480
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Video Lesson on Applications of LCM
LCM of 120 and 160 Solved Example
The product of two numbers is 19200. If their GCD is 40, what is their LCM?
Solution:
Given: GCD = 40
product of numbers = 19200
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 19200/40
Therefore, the LCM is 480.
The probable combination for the given case is LCM(120, 160) = 480.
Frequently Asked Questions on LCM of 120 and 160
What is the LCM of 120 and 160?
List the methods used to find the LCM of 120 and 160.
What is the Relation Between GCF and LCM of 120, 160?
What is the Least Perfect Square Divisible by 120 and 160?
LCM of 120 and 160 = 2 × 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5] ⇒ Least perfect square divisible by each 120 and 160 = LCM(120, 160) × 2 × 3 × 5 = 14400 [Square root of 14400 = √14400 = ±120] Therefore, 14400 is the required number.
If the LCM of 160 and 120 is 480, Find its GCF.
Since the LCM of 160 and 120 = 480
⇒ 480 × GCF(160, 120) = 19200
Therefore, the greatest common factor = 19200/480 = 40.
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