LCM of 18 and 28 is 252. The least common multiple denotes the smallest positive integer, which is multiple in a given set of numbers. The experienced faculty designed the article Least Common Multiple (LCM) to provide the best study guide for students. By mastering the LCM concept, performing well in the exams will be easy for the students. Here, we will learn how to verify the least common multiple of 18 and 28 using solved examples and FAQs in a comprehensive manner.
What is LCM of 18 and 28?
The Least Common Multiple of 18 and 28 is 252.
How to Find LCM of 18 and 28?
The LCM of 18 and 28 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 18 and 28 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Therefore, the numbers 18 and 28 can be expressed as;
18 = 2 × 3 × 3
28 = 2 × 2 × 7
LCM (18, 28) = 2 × 2 × 3 × 3 × 7 = 252
LCM of 18 and 28 Using Division Method
In the division method, we divide the numbers 18 and 28 by a common prime number until the remainder is a prime number or one. The product of these divisors denotes the least common multiple of 18 and 28.
| 2 | 18 | 28 |
| 2 | 9 | 14 |
| 3 | 9 | 7 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (18, 28) = 2 × 2 × 3 × 3 × 7 = 252
LCM of 18 and 28 Using Listing the Multiples
In this method, we list down the multiples of each number until the first common multiple is found among them. Let us glance at the multiples of 18 and 28 mentioned below.
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, …………, 216, 234, 252, …….
Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, ……..
LCM (18, 28) = 252
Related Articles
- Prime Factorisation and Division Method for LCM and HCF
- LCM Calculator
- HCF and LCM
- LCM with Examples
- LCM of Two Numbers
- LCM Formula
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 18 and 28?
Solution: 252 is the smallest number that is divisible by both 18 and 28.
2. The GCD and LCM of the two numbers are 2 and 252. If one number is 18, calculate the other number.
Solution: Let the other number be z.
We know that,
GCD × LCM = 18 × z
z = (GCD × LCM) / 18
z = (2 × 252) / 18
z = 28
Hence, the other number is 28.
Frequently Asked Questions on LCM of 18 and 28
What is the LCM of 18 and 28?
Write the LCM of 18 and 28 and the HCF of 18 and 28.
452 is the LCM of 18 and 28. True or False.
What are the methods used to find the LCM of 18 and 28?
We can find the LCM of 18 and 28 using the methods given below
Prime Factorisation
Division Method
Listing the Multiples
If the LCM of 18 and 28 is 252, what is their GCF?
GCF × LCM = 18 × 28
Given
LCM = 252
GCF × 252 = 18 × 28
GCF = 2
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