LCM of 24 and 45 is 360. LCM is the method to find the smallest possible multiple of two or more numbers. By going through the article LCM of Two Numbers, students will get to know a better way of representing the least common multiple of the given numbers more effectively, which will help them to score high marks in exams. Whenever students find themselves stuck somewhere, they can refer to this article and understand the LCM concept. Let us understand the easy method of finding the least common multiple of 24 and 45 using prime factorisation, division method and a list of multiples in this article.
What is LCM of 24 and 45?
The Least Common Multiple of 24 and 45 is 360.
How to Find LCM of 24 and 45?
LCM of 24 and 45 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 24 and 45 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 24 and 45 can be expressed as;
24 = 2 × 2 × 2 × 3
45 = 3 × 3 × 5
LCM (24, 45) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 24 and 45 Using Division Method
In the division method, to calculate the least common multiple of 24 and 45, we divide the numbers 24 and 45 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 24 and 45.
| 2 | 24 | 45 |
| 2 | 12 | 45 |
| 2 | 6 | 45 |
| 3 | 3 | 45 |
| 3 | 1 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (24, 45) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 24 and 45 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. Check the multiples of 24 and 45 mentioned below.
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240,…………, 312, 336, 360,………….
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, ……..
LCM (24, 45) = 360
Related Articles
- Least Common Multiple (LCM)
- HCF and LCM
- Prime Factorization and Division Method for LCM and HCF
- LCM Calculator
- LCM with Examples
- LCM Formula
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 24 and 45?
Solution: 360 is the smallest number that is divisible by both 24 and 45.
2. What is the LCM if the product of two numbers is 1080 and their GCD is 3?
Solution: Given
GCD = 3
Product of numbers = 1080
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 1080 / 3
LCM = 360
Therefore the LCM is 360.
Frequently Asked Questions on LCM of 24 and 45
What is the LCM of 24 and 45?
Is the LCM of 24 and 45 and the HCF of 24 and 45 are same?
260 is the LCM of 24 and 45. True or False.
What are the methods used to find the LCM of 24 and 45?
The methods to find the LCM of 24 and 45 are
Prime Factorisation
Division Method
Listing the Multiples
Find the GCF if the LCM of 24 and 45 is 360.
GCF × LCM = 24 × 45
Given
LCM = 360
GCF × 360 = 24 × 45
GCF = 3
Comments