LCM of 24 and 50 is 600. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Between all common multiples of 24 and 50, the LCM of 24 and 50 is the smallest number. (24, 48, 72, 96, 120, 144, and so on) and (50, 100, 150, 200, 250, 300, 350, and so on) are the first few multiples of 24 and 50, respectively. Listing multiples, division technique, and prime factorization are three typical ways for determining the LCM of 24 and 50.
Also read: Least common multiple
What is LCM of 24 and 50?
The answer to this question is 600. The LCM of 24 and 50 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 50, is the smallest positive integer 600 which is divisible by both 24 and 50 with no remainder.
How to Find LCM of 24 and 50?
LCM of 24 and 50 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24 and 50 Using Prime Factorisation Method
The prime factorisation of 24 and 50, respectively, is given by:
24 = 2 x 2 x 2 x 3 = 2³x 31
50 = (2 × 5 × 5) = 21 × 52
LCM (24, 50) = 600
LCM of 24 and 50 Using Division Method
We’ll divide the numbers (24, 50) by their prime factors to get the LCM of 24 and 50 using the division method (preferably common). The LCM of 24 and 50 is calculated by multiplying these divisors.
| 2 | 24 | 50 |
| 2 | 12 | 25 |
| 2 | 6 | 25 |
| 3 | 3 | 25 |
| 5 | 1 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (24, 50) = 600
LCM of 24 and 50 Using Listing the Multiples
To calculate the LCM of 24 and 50 by listing out the common multiples, list the multiples as shown below.
| Multiples of 24 | Multiples of 50 |
| 24 | 50 |
| 48 | 100 |
| 72 | 150 |
| … | …… |
| 600 | 600 |
The smallest common multiple of 24 and 50 is 600.
Therefore LCM (24, 50) = 600
Related Articles
Video Lesson on Applications of LCM
LCM of 24 and 50 Solved Example
Find the smallest number that is divisible by 24 and 50 exactly.
Solution:
The value of LCM(24, 50) will be the smallest number that is exactly divisible by 24 and 50.
⇒ Multiples of 24 and 50:
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, . . . ., 552, 576, 600, . . . .
Multiples of 50 = 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, . . . ., 450, 500, 550, 600, . . . Therefore, the LCM of 24 and 50 is 600.
Frequently Asked Questions on LCM of 24 and 50
What is the LCM of 24 and 50?
List the methods used to find the LCM of 24 and 50.
What is the Least Perfect Square Divisible by 24 and 50?
LCM of 24 and 50 = 2 × 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 2, 3] ⇒ Least perfect square divisible by each 24 and 50 = LCM(24, 50) × 2 × 3 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
What is the Relation Between GCF and LCM of 24, 50?
If the LCM of 50 and 24 is 600, Find its GCF.
Since the LCM of 50 and 24 = 600
⇒ 600 × GCF(50, 24) = 1200
Therefore, the GCF (greatest common factor) = 1200/600 = 2.
Comments