LCM of 40, 48 and 45 is 720. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. LCM of 40, 48, and 45 is the smallest number among all common multiples of 40, 48, and 45. The first few multiples of 40, 48, and 45 are (40, 80, 120, 160, 200 . . .), (48, 96, 144, 192, 240 . . .), and (45, 90, 135, 180, 225 . . .) respectively. There are 3 commonly used methods to find LCM of 40, 48, 45 – by listing multiples, by division method, and by prime factorization. Prime factorization, listing multiples, and division are the three most frequent methods for determining the LCM of 40, 48, and 45.
Also read: Least common multiple
What is LCM of 40, 48 and 45?
The answer to this question is 720. The LCM of 40, 48 and 45 using various methods is shown in this article for your reference. The LCM of three non-zero integers, 40, 48 and 45, is the smallest positive integer 720 which is divisible by both 40, 48 and 45 with no remainder.
How to Find LCM of 40, 48 and 45?
LCM of 40, 48 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40, 48 and 45 Using Prime Factorisation Method
The prime factorisation of 40, 48 and 45, respectively, is given by:
(2 × 2 × 2 × 5) = 23 × 51,
(2 × 2 × 2 × 2 × 3) = 24 × 31,
and (3 × 3 × 5) = 32 × 51
LCM (40, 48, 45) = 720
LCM of 40, 48 and 45 Using Division Method
We’ll divide the numbers (40, 48, 45) by their prime factors to get the LCM of 40, 48 and 45 using the division method (preferably common). The LCM of 40, 48 and 45 is calculated by multiplying these divisors.
| 2 | 40 | 48 | 45 |
| 2 | 20 | 24 | 45 |
| 2 | 10 | 12 | 45 |
| 2 | 5 | 6 | 45 |
| 3 | 5 | 3 | 45 |
| 5 | 5 | 1 | 15 |
| 5 | 1 | 1 | 3 |
| 3 | 1 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (40, 48, 45) = 720
LCM of 40, 48 and 45 Using Listing the Multiples
To calculate the LCM of 40, 48 and 45 by listing out the common multiples, list the multiples as shown below
| Multiples of 40 | Multiples of 48 | Multiples of 45 |
| 40 | 48 | 45 |
| 80 | 96 | 90 |
| 120 | 144 | 135 |
| 160 | 192 | 180 |
| 200 | 240 | 225 |
| 240 | …. | ….. |
| 280 | ……. | ……. |
| …. | …….. | …….. |
| 720 | 720 | 720 |
The smallest common multiple of 40, 48 and 45 is 720.
LCM (40, 48, 45) = 720
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LCM of 40, 48 and 45 Solved Example
Find the smallest number that is divisible by 40, 48, 45 exactly.
Solution:
The value of LCM(40, 48, 45) will be the smallest number that is exactly divisible by 40, 48, and 45.
⇒ Multiples of 40, 48, and 45:
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 600, 640, 680, 720, . . . .
Multiples of 48 = 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, . . . ., 528, 576, 624, 672, 720, . . . .
Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, . . . ., 540, 585, 630, 675, 720, . . . .
Therefore, the LCM of 40, 48, and 45 is 720.
Frequently Asked Questions on LCM of 40, 48 and 45
What is the LCM of 40, 48 and 45?
What are the Methods to Find LCM of 40, 48, 45?
What is the Least Perfect Square Divisible by 40, 48, and 45?
LCM of 40, 48, and 45 = 2 × 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5] ⇒ Least perfect square divisible by each 40, 48, and 45 = LCM(40, 48, 45) × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
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