LCM of 27 and 36 is 108. The smallest number among all common multiples of 27 and 36 is the LCM of 27 and 36. (27, 54, 81, 108, 135, 162, 189, etc.) and (36, 72, 108, 144, 180, 216, 252, etc.) are the first few multiples of 27 and 36, respectively. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. Various approaches, such as prime factorisation, division, and listing the multiples, can be used to quickly find the LCM.
Also read: Least common multiple
What is LCM of 27 and 36?
The answer to this question is 108. The LCM of 27 and 36 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 27 and 36, is the smallest positive integer 108 which is divisible by both 27 and 36 with no remainder.
How to Find LCM of 27 and 36?
LCM of 27 and 36 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 27 and 36 Using Prime Factorisation Method
The prime factorisation of 27 and 36, respectively, is given by:
27 = (3 × 3 × 3) = 33 and
36 = (2 × 2 × 3 × 3) = 22 × 32
LCM (24, 36) = 72
LCM of 27 and 36 Using Division Method
We’ll divide the numbers (27, 36) by their prime factors to get the LCM of 27 and 36 using the division method (preferably common). The LCM of 27 and 36 is calculated by multiplying these divisors.
| 2 | 27 | 36 |
| 2 | 27 | 18 |
| 3 | 27 | 9 |
| 3 | 9 | 3 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (27, 36) = 72
LCM of 27 and 36 Using Listing the Multiples
To calculate the LCM of 27 and 36 by listing out the common multiples, list the multiples as shown below
| Multiples of 27 | Multiples of 36 |
| 24 | 36 |
| 54 | 72 |
| 81 | 108 |
| 108 | 144 |
| 144 | – |
The smallest common multiple of 27 and 36 is 108.
Therefore LCM (27, 36) = 108
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LCM of 27 and 36 Solved Examples
Question: Find the smallest number that is divisible by 27 and 36 exactly.
Solution:
The smallest number that is divisible by 27 and 36 exactly is their LCM.
⇒ Multiples of 27 and 36:
Multiples of 27 = 27, 54, 81, 108, 135, 162, 189, . . . .
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, . . . .
Therefore, the LCM of 27 and 36 is 108.
Frequently Asked Questions on LCM of 27 and 36
What is the LCM of 27 and 36?
Which of the following is the LCM of 27 and 36? 12, 2, 25, 108
If the LCM of 36 and 27 is 108, Find its GCF.
Since the LCM of 36 and 27 = 108
⇒ 108 × GCF(36, 27) = 972
Therefore, the greatest common factor (GCF) = 972/108 = 9.
What is the Least Perfect Square Divisible by 27 and 36?
LCM of 27 and 36 = 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 3] ⇒ Least perfect square divisible by each 27 and 36 = LCM(27, 36) × 3 = 324 [Square root of 324 = √324 = ±18] Therefore, 324 is the required number.
How to Find the LCM of 27 and 36 by Prime Factorization?
⇒ LCM of 27, 36 = 22 × 32 = 108.
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