LCM of 36 and 54 is 108. The common multiples of the numbers 36 and 48 which are divisible evenly by the given numbers is the LCM. LCM of 36 and 54 is the smallest number among all common multiples of 36 and 54. The first few multiples of 36 and 54 are (36, 72, 108, 144, 180, 216, . . . ) and (54, 108, 162, 216, 270, 324, . . . ) respectively. You can make use of methods such as division, prime factorisation and listing of multiples to obtain the LCM.
What is LCM of 36 and 54?
The answer to this question is 108. The LCM of 36 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 54, is the smallest positive integer 108 which is divisible by both 36 and 54 with no remainder.
Also read: Least common multiple
How to Find LCM of 36 and 54?
LCM of 36 and 54 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 54 Using Prime Factorisation Method
The prime factorisation of 36 and 54, respectively, is given by:
36 = (2 × 2 × 3 × 3) = 22 × 32 and
54 = (2 × 3 × 3 × 3) = 21 × 33
LCM (36, 54) = 90
LCM of 36 and 54 Using Division Method
We’ll divide the numbers (36, 54) by their prime factors to get the LCM of 36 and 54 using the division method (preferably common). The LCM of 36 and 54 is calculated by multiplying these divisors.
| 2 | 36 | 54 |
| 2 | 18 | 27 |
| 3 | 9 | 27 |
| 3 | 3 | 9 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (36, 54) = 108
LCM of 36 and 54 Using Listing the Multiples
To calculate the LCM of 36 and 54 by listing out the common multiples, list the multiples as shown below:
| Multiples of 36 | Multiples of 54 |
| 36 | 54 |
| 72 | 108 |
| 108 | 162 |
| 144 | 216 |
| 180 | 270 |
The smallest common multiple of 36 and 54 is 108.
LCM (36, 54) = 108
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LCM of 36 and 54 Solved Example
Question: Find the smallest number that is divisible by 36 and 54 exactly.
Solution:
The smallest number that is divisible by 36 and 54 exactly is their LCM.
Multiples of 36 and 54:
Multiples of 36 = 36, 72, 108, 144, 180, . . . .
Multiples of 54 = 54, 108, 162, 216, 270, . . . .
Therefore, the LCM of 36 and 54 is 108.
Frequently Asked Questions on LCM of 36 and 54
What is the LCM of 36 and 54?
List the methods used to find the LCM of 36 and 54.
If the LCM of 54 and 36 is 108, Find its GCF.
Since the LCM of 54 and 36 = 108
⇒ 108 × GCF(54, 36) = 1944
Therefore, the GCF (greatest common factor) = 1944/108 = 18.
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