LCM of 18 and 24 is 72. The smallest common multiple of two or more numbers is known as Least common multiple. Go through the article of LCM of Two Numbers to grasp the proper understanding on LCM which is very important to achieve remarkable grades in exams. Prime factorisation, division method and listing multiples are the three methods which are used to find the LCM. Let us learn how to find the least common multiple of 18 and 24 in a precise manner in this article.
What is LCM of 18 and 24?
The answer to this question is 72.
How to Find LCM of 18 and 24?
LCM of 18 and 24 can be determined by using the three methods shown below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 24 Using Prime Factorisation Method
By prime factorisation method, we can write 18 and 24 as the product of prime numbers, such that;
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
LCM (18, 24) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 18 and 24 Using Division Method
In this method, we divide the numbers 18 and 24 by their prime factors to calculate their LCM. The product of these divisors depicts the least common multiple of 18 and 24. This can be shown as below.
|
2 |
18 |
24 |
|
2 |
9 |
12 |
|
2 |
9 |
6 |
|
3 |
9 |
3 |
|
3 |
3 |
1 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (18, 24) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 18 and 24 Using Listing the Multiples
Here we list out the multiples of 18 and 24 to determine their least common multiple as shown below:
|
Multiples of 18 |
Multiples of 24 |
|
18 |
24 |
|
36 |
48 |
|
54 |
72 |
|
72 |
96 |
|
90 |
120 |
|
108 |
144 |
LCM (18, 24) = 72
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: Calculate the number if GCD and LCM of two numbers are 6 and 72 and one of the numbers is 24.
Solution: Let the required number be r
WKT
GCD × LCM = 24 × r
r = (GCD × LCM)/24
r = (6 × 72)/24
r = 18
Hence the required number is 18.
Q. 2: Find the LCM of 18 and 24 by prime factorisation.
Solution: 18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
LCM of 18 and 24 = 2 × 2 × 2 × 3 × 3 = 72
Therefore the LCM of 18 and 24 by prime factorisation is 72.
Frequently Asked Questions on LCM of 18 and 24
What is the LCM of 18 and 24?
Name the methods used to determine the LCM of 18 and 24.
There are three methods used to determine the LCM of 18 and 24. They are as follows:
Prime Factorisation
Division Method
Listing the multiples
Comments