LCM of 3, 9 and 15 is 45. In Maths, LCM is defined as the smallest common multiple of two or more numbers. The article LCM of Two Numbers is the best reference material drafted by subject matter experts to gain knowledge and command over the LCM concept. Utilising this article on a regular basis help students solve any problem based on the LCM with speed and correctness. Let us grasp the simple method of how to find the least common multiple of 3, 9 and 15 using prime factorisation, division method and a list of multiples here.
What is LCM of 3, 9 and 15?
The Least Common Multiple of 3, 9 and 15 is 45.
How to Find LCM of 3, 9 and 15?
LCM of 3, 9 and 15 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 3, 9 and 15 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 3, 9 and 15 can be expressed as;
3 = 3
9 = 3 × 3
15 = 3 × 5
LCM (3, 9, 15) = 3 × 3 × 5 = 45
LCM of 3, 9 and 15 Using Division Method
In the division method, to calculate the least common multiple of 3, 9 and 15, we divide the numbers 3, 9 and 15 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 3, 9 and 15.
| 3 | 3 | 9 | 15 |
| 3 | 1 | 3 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (3, 9, 15) = 3 × 3 × 5 = 45
LCM of 3, 9 and 15 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 3, 9 and 15 mentioned below.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ……….., 39, 42, 45, ………..
Multiples of 9: 9, 18, 27, 36, 45, ………..
Multiples of 15: 15, 30, 45, ……………
LCM (3, 9, 15) = 45
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 3, 9, 15 exactly?
Solution: The smallest number that is divisible by 3, 9, 15 exactly is their LCM. The LCM of 3, 9 and 15 is 45. Hence the smallest number that is divisible by 3, 9, 15 exactly is 45.
Frequently Asked Questions on LCM of 3, 9 and 15
What is the LCM of 3, 9 and 15?
Mention the LCM of 3, 9 and 15 and the HCF of 3, 9 and 15.
55 is the LCM of 3, 9 and 15. True or False.
Name the methods used to find the LCM of 3, 9 and 15.
The following methods can be used to find the LCM of 3, 9 and 15
Prime Factorisation
Division Method
Listing the Multiples
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