LCM of 15 and 30 is 30. We can find the LCM of given numbers using prime factorisation, division method and listing multiples easily. The article LCM of Two Numbers is designed by faculty to help students understand how to verify the LCM of two numbers effortlessly. Following this article while solving problems undoubtedly enhances the conceptual knowledge among students. Learn how to calculate the least common multiple of 15 and 30 with the help of examples and FAQs in simple language in this article.
What is LCM of 15 and 30?
The Least Common Multiple of 15 and 30 is 30.
How to Find LCM of 15 and 30?
The following methods can be used to verify the LCM of 15 and 30 in an easy manner.
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 30 Using Prime Factorisation Method
By prime factorisation method, we can write 15 and 30 as the product of prime numbers, such that;
15 = 3 × 5
30 = 2 × 3 × 5
LCM (15, 30) = 2 × 3 × 5 = 30
LCM of 15 and 30 Using Division Method
In this method, we divide the numbers 15 and 30 by their prime factors to calculate their LCM. The product of these divisors denotes the least common multiple of 15 and 30.
|
2 |
15 |
30 |
|
3 |
15 |
15 |
|
5 |
5 |
5 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (15, 30) = 2 × 3 × 5 = 30
LCM of 15 and 30 Using Listing the Multiples
Here we list out the multiples of 15 and 30 to find their least common multiple as shown below:
|
Multiples of 15 |
Multiples of 30 |
|
15 |
30 |
|
30 |
60 |
|
45 |
90 |
|
60 |
120 |
|
75 |
150 |
LCM (15, 30) = 30
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: Find the smallest number that is divisible by both 15 and 30.
Solution: 30 is the smallest number that is divisible by both 15 and 30.
Q. 2: Find the LCM of 15 and 30 using the prime factorisation method.
Solution: We find the LCM of 15 and 30 by prime factorisation as below:
15 = 3 × 5
30 = 2 × 3 × 5
LCM (15, 30) = 2 × 3 × 5 = 30
Hence, the LCM of 15 and 30 is 30.
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