LCM of 30 and 36 is 180. The lowest common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. Least Common Multiple (LCM) is the best reference guide designed by experts for the students to solve problems based on the LCM concept effortlessly. Following this article on a regular basis not only clears doubts of students but also helps them to build skills which are essential to score well in exams. In this article, we will discuss how to find the least common multiple of 30 and 36 in a descriptive manner.
What is LCM of 30 and 36?
The Least Common Multiple of 30 and 36 is 180.
How to Find LCM of 30 and 36?
We can find the LCM of 30 and 36 by using the methods given below:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 30 and 36 Using Prime Factorisation Method
In the prime factorisation method, LCM of 30 and 36 can be obtained by multiplying the prime factors raised to their respective highest power.
30 = 2 × 3 × 5
36 = 2 × 2 × 3 × 3
LCM (30, 36) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 30 and 36 Using Division Method
In the division method, to calculate the LCM, we divide the numbers 30 and 36 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 30 and 36.
| 2 | 30 | 36 |
| 2 | 15 | 18 |
| 3 | 15 | 9 |
| 3 | 5 | 3 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (30, 36) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 30 and 36 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the least common multiple among them. Let us have a look at the multiples of 30 and 36 from the table given below.
| Multiples of 30 | Multiples of 36 |
| 30 | 36 |
| 60 | 72 |
| 90 | 108 |
| 120 | 144 |
| 150 | 180 |
| 180 | 216 |
| 210 | 252 |
LCM (30, 36) = 180
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 30 and 36?
Solution: 180 is the smallest number that is divisible by both 30 and 36.
2. What is the lowest common factor of 30 and 36?
Solution: The lowest common factor of 30 and 36 is 180.
Frequently Asked Questions on LCM of 30 and 36
What is the LCM of 30 and 36?
What is the difference between the LCM of 30 and 36 and the HCF of 30 and 36?
Mention the methods used to find the LCM of 30 and 36.
The methods used to find the LCM of 30 and 36 are as follows:
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 30 and 36 using prime factorisation method.
To find the LCM using prime factorisation, we express the given numbers as the product of prime factors
30 = 2 × 3 × 5
36 = 2 × 2 × 3 × 3
LCM (30, 36) = 2 × 2 × 3 × 3 × 5 = 180
What is the GCF if the LCM of 30 and 36 is 180?
GCF × LCM = 30 × 36
Given
LCM = 180
GCF × 180 = 30 × 36
GCF = 6
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