LCM of 108 and 144 is 432. LCM stands for least common multiple in Mathematics. It is also known as LCD. The article HCF and LCM is the best study resource for students to understand the LCM and HCF concepts more effectively. Students are recommended to follow this article while solving problems to sharpen their problem-solving and logical thinking skills. This also helps them to obtain excellent scores in the examinations. In this article, we will study how to calculate the least common multiple of 108 and 144 in an efficient way.
What is LCM of 108 and 144?
The Least Common Multiple of 108 and 144 is 432.
How to Find LCM of 108 and 144?
We can obtain the LCM of 108 and 144 by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 108 and 144 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 108 and 144 can be expressed as;
108 = 2 × 2 × 3 × 3 × 3
144 = 2 × 2 × 2 × 2 × 3 × 3
LCM (108, 144) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 108 and 144 Using Division Method
In the division method, we divide the numbers 108 and 144 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 108 and 144.
| 2 | 108 | 144 |
| 2 | 54 | 72 |
| 2 | 27 | 36 |
| 2 | 27 | 18 |
| 3 | 27 | 9 |
| 3 | 9 | 3 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No more further division can be done.
Therefore, LCM (108, 144) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 108 and 144 Using Listing the Multiples
In this method, we list out the multiples of given natural numbers to find the lowest common multiple among them. The following table depicts the multiples of 108 and 144.
| Multiples of 108 | Multiples of 144 |
| 108 | 144 |
| 216 | 288 |
| 324 | 432 |
| 432 | 576 |
| 540 | 720 |
LCM (108, 144) = 432
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 108 and 144?
Solution: 432 is the smallest number that is divisible by both 108 and 144.
2. What are the first five multiples of 108 and 144?
Solution: The first five multiples of 108 and 144 are as follows:
Multiples of 108 = 108, 216, 324, 432, and 540
Multiples of 144 = 144, 288, 432, 576, and 720
Frequently Asked Questions on LCM of 108 and 144
What is the LCM of 108 and 144?
What is the difference between the LCM of 108 and 144 and the HCF of 108 and 144?
Is 56 the greatest common factor of 108 and 144?
If the LCM of 108 and 144 is 432. Calculate the GCF.
GCF × LCM = 108 × 144
Given
LCM = 432
GCF × 432 = 108 × 144
GCF = 36
Mention the relation between GCF and LCM of 108 and 144.
The relation between GCF and LCM of 108 and 144 is
GCF × LCM = 108 × 144
GCF × LCM = 15552
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