The LCM of 24 and 30 is 120. The Lowest Common Multiple (LCM) is a fundamental concept in mathematics that simplifies operations such as adding and subtracting fractions. It's crucial to understand the concept of LCM to make arithmetic problems easier to solve. We recommend students to refer to the article Prime Factorisation and Division Method for LCM and HCF to efficiently find the LCM and HCF of given numbers. In this article, we will learn a simple method to find the least common multiple of 24 and 30.
LCM of 24 and 30 - Prime Factorisation, Division Method, Listing Multiples
Last Updated on Jun 07, 2024
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What is the LCM of 24 and 30?
The LCM of 24 and 30 is 120.
How to Calculate the LCM of 24 and 30?
The LCM of 24 and 30 can be calculated using the following methods:
- Prime Factorisation
- Division method
- Listing multiples
Finding the LCM of 24 and 30 Using the Prime Factorisation Method
The prime factorisation method allows us to express 24 and 30 as a product of prime numbers. For example:
24 = 2 × 2 × 2 × 3
30 = 2 × 3 × 5
LCM (24, 30) = 2 × 2 × 2 × 3 × 5 = 120
Finding the LCM of 24 and 30 Using the Division Method
In this method, we divide the numbers 24 and 30 by their prime factors to find their LCM. The product of these divisors gives the least common multiple of 24 and 30.
|
2 |
24 |
30 |
|
2 |
12 |
15 |
|
2 |
6 |
15 |
|
3 |
3 |
15 |
|
5 |
1 |
5 |
|
x |
1 |
1 |
No further division is possible.
Therefore, LCM (24, 30) = 2 × 2 × 2 × 3 × 5 = 120
Finding the LCM of 24 and 30 by Listing the Multiples
To find the least common multiple of 24 and 30 by listing multiples, we list the multiples of 24 and 30 as shown below:
|
Multiples of 24 |
Multiples of 30 |
|
24 |
30 |
|
48 |
60 |
|
72 |
90 |
|
96 |
120 |
|
120 |
150 |
|
144 |
180 |
LCM (24, 30) = 120
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Frequently Asked Questions
What is the LCM of 24 and 30?
The LCM of 24 and 30 is 120.
Is the LCM of 24 and 30 the same as the HCF of 24 and 30?
No. LCM of 24 and 30 is 120 and HCF of 24 and 30 is 6.
140 is the LCM of 24 and 30. True or False.
False. The LCM of 24 and 30 is 120.
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