LCM of 36, 48 and 54 is 432. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 36, 48, and 54 is the LCM of 36, 48, and 54. (36, 72, 108, 144, 180…), (48, 96, 144, 192, 240…), and (54, 108, 162, 216, 270…), respectively, are the first few multiples of 36, 48, and 54. There are three typical ways for calculating the LCM of 36, 48, and 54: listing multiples, prime factorization, and division.
Also read: Least common multiple
What is LCM of 36, 48 and 54?
The answer to this question is 432. The LCM of 36, 48 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36, 48 and 54, is the smallest positive integer 432 which is divisible by both 36, 48 and 54 with no remainder.
How to Find LCM of 36, 48 and 54?
LCM of 36, 48 and 54 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36, 48 and 54 Using Prime Factorisation Method
The prime factorisation of 36, 48 and 54, respectively, is given by:
36 = (2 × 2 × 3 × 3) = 22 × 32,
48 = (2 × 2 × 2 × 2 × 3) = 24 × 31, and
54 = (2 × 3 × 3 × 3) = 21 × 33
LCM (36, 48, 54) = 432
LCM of 36, 48 and 54 Using Division Method
We’ll divide the numbers (36, 48, 54) by their prime factors to get the LCM of 36, 48 and 54 using the division method (preferably common). The LCM of 36, 48 and 54 is calculated by multiplying these divisors.
| 2 | 36 | 48 | 54 |
| 2 | 18 | 24 | 27 |
| 2 | 9 | 12 | 27 |
| 2 | 9 | 6 | 27 |
| 3 | 3 | 3 | 27 |
| 3 | 1 | 1 | 9 |
| 3 | 1 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (36, 48, 54) = 342
LCM of 36, 48 and 54 Using Listing the Multiples
To calculate the LCM of 36, 48 and 54 by listing out the common multiples, list the multiples as shown below
| Multiples of 36 | Multiples of 48 | Multiples of 54 |
| 36 | 48 | 54 |
| 72 | 96 | 108 |
| 108 | 144 | 162 |
| …. | ….. | ….. |
| 342 | 342 | 342 |
The smallest common multiple of 36, 48 and 54 is 342.
Therefore LCM (36, 48, 54) = 342
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LCM of 36, 48 and 54 Solved Example
Find the smallest number that is divisible by 36, 48, 54 exactly.
Solution:
The smallest number that is divisible by 36, 48, and 54 exactly is their LCM.
⇒ Multiples of 36, 48, and 54:
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, . . . .
Multiples of 48 = 48, 96, 144, 192, 240, 288, 336, 384, 432, . . . .
Multiples of 54 = 54, 108, 162, 216, 270, 324, 378, 432, . . . .
Therefore, the LCM of 36, 48, and 54 is 432.
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