LCM of 3 and 27 is 27. The smallest number among all common multiples of 3 and 27 is the LCM of 3 and 27. (3, 6, 9, 12,… ) and (27, 54, 81, 108, 135,… ) are the first few multiples of 3 and 27, respectively. To find the LCM of 3 and 27, there are three typical methods: prime factorization, division method, and listing multiples. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 3 and 27?
The answer to this question is 27. The LCM of 3 and 27 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 27, is the smallest positive integer 27 which is divisible by both 3 and 27 with no remainder.
How to Find LCM of 3 and 27?
LCM of 3 and 27 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3 and 27 Using Prime Factorisation Method
The prime factorisation of 3 and 27, respectively, is given by:
(3) = 31 and
27 = (3 × 3 × 3) = 33
LCM (3, 27) = 27
LCM of 3 and 27 Using Division Method
We’ll divide the numbers (3, 27) by their prime factors to get the LCM of 3 and 27 using the division method (preferably common). The LCM of 3 and 27 is calculated by multiplying these divisors.
| 3 | 3 | 27 |
| 3 | 1 | 9 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (3, 27) = 27
LCM of 3 and 27 Using Listing the Multiples
To calculate the LCM of 3 and 27 by listing out the common multiples, list the multiples as shown below
| Multiples of 3 | Multiples of 27 |
| 3 | 27 |
| 6 | 54 |
| 9 | 81 |
| …. | 108 |
| 27 | 135 |
The smallest common multiple of 3 and 27 is 27.
Therefore LCM (3, 27) = 27
Related Articles
Video Lesson on Applications of LCM
LCM of 3 and 27 Solved Example
The product of two numbers is 81. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 81
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 81/3
Therefore, the LCM is 27.
The probable combination for the given case is LCM(3, 27) = 27.
Frequently Asked Questions on LCM of 3 and 27
What is the LCM of 3 and 27?
List the methods used to find the LCM of 3 and 27.
If the LCM of 27 and 3 is 27, Find its GCF.
Since the LCM of 27 and 3 = 27
⇒ 27 × GCF(27, 3) = 81
Therefore, the greatest common factor (GCF) = 81/27 = 3.
What is the Relation Between GCF and LCM of 3, 27?
What is the Least Perfect Square Divisible by 3 and 27?
LCM of 3 and 27 = 3 × 3 × 3 [Incomplete pair(s): 3] ⇒ Least perfect square divisible by each 3 and 27 = LCM(3, 27) × 3 = 81 [Square root of 81 = √81 = ±9] Therefore, 81 is the required number.
Comments