LCM of 25, 40 and 60 is 600. LCM of 25, 40, and 60 is the smallest number among all common multiples of 25, 40, and 60. The first few multiples of 25, 40, and 60 are (25, 50, 75, 100, 125 . . .), (40, 80, 120, 160, 200 . . .), and (60, 120, 180, 240, 300 . . .) respectively. 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.
Also read: Least common multiple
What is LCM of 25, 40 and 60?
The answer to this question is 600. The LCM of 25, 40 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 25, 40 and 60, is the smallest positive integer 600 which is divisible by both 25, 40 and 60 with no remainder.
How to Find LCM of 25, 40 and 60?
LCM of 25, 40 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 25, 40 and 60 Using Prime Factorisation Method
The prime factorisation of 25, 40 and 60, respectively, is given by:
25 = (5 × 5) = 52,
40 = (2 × 2 × 2 × 5) = 23 × 51, and
60 = (2 × 2 × 3 × 5) = 22 × 31 × 51
LCM (25, 40, 60) = 600
LCM of 25, 40 and 60 Using Division Method
We’ll divide the numbers (25, 40, 60) by their prime factors to get the LCM of 25, 40 and 60 using the division method (preferably common). The LCM of 25, 40 and 60 is calculated by multiplying these divisors.
| 2 | 25 | 40 | 60 |
| 2 | 25 | 20 | 30 |
| 2 | 25 | 10 | 15 |
| 3 | 25 | 5 | 15 |
| 5 | 25 | 1 | 5 |
| 5 | 5 | 1 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (25, 40, 60) = 600
LCM of 25, 40 and 60 Using Listing the Multiples
To calculate the LCM of 25, 40 and 60 by listing out the common multiples, list the multiples as shown below
| Multiples of 25 | Multiples of 40 | Multiples of 60 |
| 25 | 40 | 60 |
| 50 | 80 | 120 |
| 75 | 120 | 180 |
| 100 | 160 | 240 |
| …….. | ……. | …… |
| 600 | 600 | 600 |
The smallest common multiple of 25, 40 and 60 is 600.
Therefore LCM (25, 40, 60) = 600
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LCM of 25, 40 and 60 Solved Example
Question: Find the smallest number that is divisible by 25, 40, 60 exactly.
Solution:
The value of LCM(25, 40, 60) will be the smallest number that is exactly divisible by 25, 40, and 60.
⇒ Multiples of 25, 40, and 60:
Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 525, 550, 575, 600, . . . .
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 520, 560, 600, . . . .
Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, . . . ., 480, 540, 600, . . . .
Therefore, the LCM of 25, 40, and 60 is 600.
Frequently Asked Questions on LCM of 25, 40 and 60
What is the LCM of 25, 40 and 60?
List the methods used to find the LCM of 25, 40 and 60.
What is the Least Perfect Square Divisible by 25, 40, and 60?
LCM of 25, 40, and 60 = 2 × 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 2, 3] ⇒ Least perfect square divisible by each 25, 40, and 60 = LCM(25, 40, 60) × 2 × 3 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
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