LCM of 144, 180 and 192 is 2880. 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 frequent multiples of 144, 180, and 192 is the LCM of 144, 180, and 192. (144, 288, 432, 576, 720…), (180, 360, 540, 720, 900…), and (192, 384, 576, 768, 960…), respectively, are the first few multiples of 144, 180, and 192.
Also read: Least common multiple
What is LCM of 144, 180 and 192?
The answer to this question is 2880. The LCM of 144, 180 and 192 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 144, 180 and 192, is the smallest positive integer 2880 which is divisible by both 144, 180 and 192 with no remainder.
How to Find LCM of 144, 180 and 192?
LCM of 144, 180 and 192 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 144, 180 and 192 Using Prime Factorisation Method
The prime factorisation of 144, 180 and 192, respectively, is given by:
144 = (2 × 2 × 2 × 2 × 3 × 3) = 24 × 32,
180 = (2 × 2 × 3 × 3 × 5) = 22 × 32 × 51, and
192 = (2 × 2 × 2 × 2 × 2 × 2 × 3) = 26 × 31
LCM (144, 180, 192) = 2880
LCM of 144, 180 and 192 Using Division Method
We’ll divide the numbers LCM (144, 180, 192) by their prime factors to get the LCM of 144, 180 and 192 using the division method (preferably common). The LCM of 144, 180 and 192 is calculated by multiplying these divisors.
| 2 | 144 | 180 | 192 |
| 2 | 72 | 90 | 96 |
| 2 | 36 | 45 | 48 |
| 2 | 18 | 45 | 24 |
| 2 | 9 | 45 | 12 |
| 2 | 9 | 45 | 6 |
| 3 | 9 | 45 | 3 |
| 3 | 3 | 15 | 1 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (144, 180, 192) = 2880
LCM of 144, 180 and 192 Using Listing the Multiples
To calculate the LCM of 144, 180 and 192 by listing out the common multiples, list the multiples as shown below.
| Multiples of 144 | Multiples of 180 | Multiples of 192 |
| 144 | 180 | 192 |
| 288 | 360 | 384 |
| 432 | 540 | 576 |
| …….. | …… | ……… |
| 2880 | 2880 | 2880 |
The smallest common multiple of 144, 180 and 192 is 2880.
Therefore LCM (144, 180, 192) = 2880
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LCM of 144, 180 and 192 Solved Examples
Question: Find the smallest number that is divisible by 144, 180, 192 exactly.
Solution:
The value of LCM(144, 180, 192) will be the smallest number that is exactly divisible by 144, 180, and 192.
⇒ Multiples of 144, 180, and 192:
Multiples of 144 = 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440, . . . ., 2448, 2592, 2736, 2880, . . . .
Multiples of 180 = 180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, . . . ., 2340, 2520, 2700, 2880, . . . .
Multiples of 192 = 192, 384, 576, 768, 960, 1152, 1344, 1536, 1728, 1920, . . . ., 2304, 2496, 2688, 2880, . . . .
Therefore, the LCM of 144, 180, and 192 is 2880.
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