LCM of 6 and 27 is 54. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. Simple language is used in the article HCF and LCM so that students understand the concepts better. This article is designed with the utmost care by subject matter experts to provide the best learning experience for the students. Here, we will discuss how to calculate the least common multiple of 6 and 27 in detail.
What is LCM of 6 and 27?
The Least Common Multiple of 6 and 27 is 54.
How to Find LCM of 6 and 27?
The LCM of 6 and 27 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 6 and 27 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 6 and 27 can be represented as;
6 = 2 × 3
27 = 3 × 3 × 3
LCM (6, 27) = 2 × 3 × 3 × 3 = 54
LCM of 6 and 27 Using Division Method
In the division method, we divide the numbers 6 and 27 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 6 and 27.
| 2 | 6 | 27 |
| 3 | 3 | 27 |
| 3 | 1 | 9 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Therefore, LCM (6, 27) = 2 × 3 × 3 × 3 = 54
LCM of 6 and 27 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 6 and 27.
| Multiples of 6 | Multiples of 27 |
| 6 | 27 |
| 12 | 54 |
| 18 | 81 |
| 24 | 108 |
| 30 | 135 |
| 36 | 162 |
| 42 | 189 |
| 48 | 216 |
| 54 | 243 |
| 60 | 270 |
LCM (6, 27) = 54
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Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 6 and 27?
Solution: 54 is the smallest number that is divisible by both 6 and 27.
2. The GCD and LCM of the two numbers are 3 and 54. If one number is 27, what is the other number?
Solution: Let the other number be m
We know that,
GCD × LCM = 27 × m
m = (GCD × LCM) / 27
m = (3 × 54) / 27
m = 6
Hence, the other number is 6.
Frequently Asked Questions on LCM of 6 and 27
What is the LCM of 6 and 27?
What are the methods used to find the LCM of 6 and 27?
The following methods are used to find the LCM of 6 and 27:
Prime Factorisation
Division Method
Listing the Multiples
64 is the LCM of 6 and 27. True or False.
What is the LCM of 6 and 27 and the HCF of 6 and 27?
Find the LCM of 6 and 27 using the prime factorisation method.
In the prime factorisation method, the numbers are expressed as the product of prime factors.
6 = 2 × 3
27 = 3 × 3 × 3
LCM (6, 27) = 2 × 3 × 3 × 3 = 54
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