LCM of 40, 50 and 60 is 600. The smallest number among all common multiples of 40, 50, and 60 is the LCM of 40, 50, and 60. (40, 80, 120, 160, 200…), (50, 100, 150, 200, 250…), and (60, 120, 180, 240, 300…), respectively, are the first few multiples of 40, 50, and 60. To find the LCM of 40, 50, or 60, you can use one of three methods: listing multiples, prime factorization, or the division method. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 40, 50 and 60?
The answer to this question is 600. The LCM of 40, 50 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40, 50 and 60, is the smallest positive integer 600 which is divisible by both 40, 50 and 60 with no remainder.
How to Find LCM of 40, 50 and 60?
LCM of 40, 50 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40, 50 and 60 Using Prime Factorisation Method
The prime factorisation of 40, 50 and 60, respectively, is given by:
40 = (2 × 2 × 2 × 5) = 23 × 51,
50 = (2 × 5 × 5) = 21 × 52, and
60 = (2 × 2 × 3 × 5) = 22 × 31 × 51
LCM (40, 50, 60) = 600
LCM of 40, 50 and 60 Using Division Method
We’ll divide the numbers (40, 50, 60) by their prime factors to get the LCM of 40, 50 and 60 using the division method (preferably common). The LCM of 40, 50 and 60 is calculated by multiplying these divisors.
| 2 | 40 | 50 | 60 |
| 2 | 20 | 25 | 30 |
| 2 | 10 | 25 | 15 |
| 3 | 5 | 25 | 15 |
| 5 | 5 | 25 | 5 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (40, 50, 60) = 600
LCM of 40, 50 and 60 Using Listing the Multiples
To calculate the LCM of 40, 50 and 60 by listing out the common multiples, list the multiples as shown below
| Multiples of 40 | Multiples of 50 | Multiples of 60 |
| 40 | 50 | 60 |
| 80 | 100 | 120 |
| 120 | 150 | 180 |
| ….. | …… | …… |
| 600 | 600 | 600 |
The smallest common multiple of 40, 50 and 60 is 600.
Therefore LCM (40, 50, 60) = 600
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Video Lesson on Applications of LCM
LCM of 40, 50 and 60 Solved Example
Find the smallest number that is divisible by 40, 50, 60 exactly.
Solution:
The smallest number that is divisible by 40, 50, and 60 exactly is their LCM.
⇒ Multiples of 40, 50, and 60:
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, . . . .
Multiples of 50 = 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, . . . .
Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, . . . .
Therefore, the LCM of 40, 50, and 60 is 600.
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