LCM of 24, 36 and 54 is 216. The smallest number among all common multiples of 24, 36, and 54 is the LCM of 24, 36, and 54. (24, 48, 72, 96, 120…), (36, 72, 108, 144, 180…), and (54, 108, 162, 216, 270…), respectively, are the first few multiples of 24, 36, and 54. There are three typical ways for calculating the LCM of 24, 36, and 54: listing multiples, prime factorization, and division. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 24, 36 and 54?
The answer to this question is 216. The LCM of 24, 36 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24, 36 and 54, is the smallest positive integer 216 which is divisible by both 24, 36 and 54 with no remainder.
How to Find LCM of 24, 36 and 54?
LCM of 24, 36 and 54 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24, 36 and 54 Using Prime Factorisation Method
The prime factorisation of 24, 36 and 54, respectively, is given by:
24 = 2 x 2 x 2 x 3 = 2³x 3
36 = 2 x 2 x 3 x 3 = 2² x 3²
54 = (2 × 3 × 3 × 3) = 21 × 33
LCM (24, 36, 54) = 216
LCM of 24, 36 and 54 Using Division Method
We’ll divide the numbers (24, 36, 54) by their prime factors to get the LCM of 24, 36 and 54 using the division method (preferably common). The LCM of 24, 36 and 54 is calculated by multiplying these divisors.
| 2 | 24 | 36 | 54 |
| 2 | 12 | 18 | 27 |
| 2 | 6 | 9 | 27 |
| 2 | 3 | 9 | 27 |
| 3 | 1 | 3 | 27 |
| 3 | 1 | 1 | 9 |
| 3 | 1 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (24, 36, 54) = 216
LCM of 24, 36 and 54 Using Listing the Multiples
To calculate the LCM of 24, 36 and 54 by listing out the common multiples, list the multiples as shown below
| Multiples of 24 | Multiples of 36 | Multiples of 54 |
| 24 | 36 | 54 |
| 48 | 72 | 108 |
| 72 | 108 | 162 |
| 96 | 144 | 216 |
| … | 180 | 270 |
| 216 | 216 | 324 |
The smallest common multiple of 24, 36 and 54 is 216.
Therefore LCM (24, 36, 54) = 216
Related Articles
Video Lesson on Applications of LCM
LCM of 24, 36 and 54 Solved Example
Find the smallest number that is divisible by 24, 36, 54 exactly.
Solution:
The smallest number that is divisible by 24, 36, and 54 exactly is their LCM.
⇒ Multiples of 24, 36, and 54:
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, . . . .
Multiples of 36 = 36, 72, 108, 144, 180, 216, . . . .
Multiples of 54 = 54, 108, 162, 216, 270, . . . .
Frequently Asked Questions on LCM of 24, 36 and 54
What is the LCM of 24, 36 and 54?
List the methods used to find the LCM of 24, 36 and 54.
Which of the following is the LCM of 24, 36, and 54? 120, 100, 216, 35
What is the Least Perfect Square Divisible by 24, 36, and 54?
LCM of 24, 36, and 54 = 2 × 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 2, 3] ⇒ Least perfect square divisible by each 24, 36, and 54 = LCM(24, 36, 54) × 2 × 3 = 1296 [Square root of 1296 = √1296 = ±36] Therefore, 1296 is the required number.
Therefore, the LCM of 24, 36, and 54 is 216.
Comments