LCM of 27 and 48 is 432. LCM denotes the least common factor or multiple of any two or more given numbers. For a good grip on the LCM concept, students are advised to refer to the article LCM with Examples. This article is designed by keeping in mind the understanding abilities of students which differ from one student to the other. Let us learn how to denote the least common multiple of 27 and 48 with the help of solved examples and FAQs in this article.
What is LCM of 27 and 48?
The Least Common Multiple of 27 and 48 is 432.
How to Find LCM of 27 and 48?
LCM of 27 and 48 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 27 and 48 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 27 and 48 are expressed as;
27 = 3 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
LCM (27, 48) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 27 and 48 Using Division Method
In the division method, to find the least common multiple of 27 and 48, we divide the numbers 27 and 48 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 27 and 48.
| 2 | 27 | 48 |
| 2 | 27 | 24 |
| 2 | 27 | 12 |
| 2 | 27 | 6 |
| 3 | 27 | 3 |
| 3 | 9 | 1 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (27, 48) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 27 and 48 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. The multiples of 27 and 48 are as follows:
Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, …, 324, 351, 378, 405, 432,…
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, …., 288, 336, 384, 432, …..
LCM (27, 48) = 432
Related Articles
- Lowest Common Multiple (LCM)
- Prime Factorisation and Division Method for LCM and HCF
- LCM of Two Numbers
- LCM calculator
- LCM Formula
- HCF and LCM
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 27 and 48?
Solution: 432 is the smallest number that is divisible by both 27 and 48.
2. Find the LCM if the product of two numbers is 1296 and their GCD is 3.
Solution: Given
GCD = 3
Product of numbers = 1296
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 1296 / 3
LCM = 432
Hence the LCM is 432.
Frequently Asked Questions on LCM of 27 and 48
What is the LCM of 27 and 48?
Is the LCM of 27 and 48 the same as the HCF of 27 and 48?
Name the methods used to find the LCM of 27 and 48.
The methods used to find the LCM of 27 and 48 are:
Prime Factorisation
Division method
Listing the Multiples
Calculate the GCF if the LCM of 27 and 48 is 432.
GCF × LCM = 27 × 48
Given
LCM = 432
GCF × 432 = 27 × 48
GCF = 3
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