LCM of 28 and 48 is 336. The LCM is the method to find the least common multiple between any two or more numbers. For in-depth knowledge of the LCM concept, students must refer to the article LCM with Examples developed by experts in simple language with utmost care. Practising the problems with the help of this article makes learning the LCM concept more interesting among students. Let us learn the simple process of how to find the least common multiple of 28 and 48 in this article.
What is LCM of 28 and 48?
The Least Common Multiple of 28 and 48 is 336.
How to Find LCM of 28 and 48?
LCM of 28 and 48 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 28 and 48 Using Prime Factorisation Method
In the prime factorisation method, LCM of 28 and 48 can be obtained by multiplying prime factors raised to their respective highest power.
28 = 2 × 2 × 7
48 = 2 × 2 × 2 × 2 × 3
LCM (28, 48) = 2 × 2 × 2 × 2 × 3 × 7 = 336
LCM of 28 and 48 Using Division Method
In the division method, to determine the least common multiple of 28 and 48, we divide the numbers 28 and 48 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 28 and 48.
| 2 | 28 | 48 |
| 2 | 14 | 24 |
| 2 | 7 | 12 |
| 2 | 7 | 6 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (28, 48) = 2 × 2 × 2 × 2 × 3 × 7 = 336
LCM of 28 and 48 Using Listing the Multiples
In this method, we list down the multiples of 28 and 48 to find the least common multiple among them. Below is the list of multiples of 28 and 48.
Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, ………..
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, ………
LCM (28, 48) = 336
Related Articles
- Least Common Multiple (LCM)
- Prime Factorisation and Division Method for LCM and HCF
- LCM of Two Numbers
- HCF and LCM
- LCM calculator
- LCM Formula
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 28 and 48?
Solution: 336 is the smallest number that is divisible by both 28 and 48.
2. The GCD and LCM of the two numbers are 4 and 336. If one number is 48, calculate the other number.
Solution: Let the other number be r
We know that,
GCD × LCM = 48 × r
r = (GCD × LCM) / 48
r = (4 × 336) / 48
r = 28
Hence the other number is 28.
Frequently Asked Questions on LCM of 28 and 48
What is the LCM of 28 and 48?
Is the LCM of 28 and 48 the same as the HCF of 28 and 48?
Name the methods used to find the LCM of 28 and 48.
The methods used to find the LCM of 28 and 48 are as follows:
Prime Factorisation
Division method
Listing the Multiples
What is the GCF if the LCM of 28 and 48 is 336?
GCF × LCM = 28 × 48
Given
LCM = 336
GCF × 336 = 28 × 48
GCF = 4
Mention the relation between GCF and LCM of 28 and 48.
The equation used to express the relation between GCF and LCM of 28 and 48 is
GCF × LCM = 28 × 48
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