LCM of 3 and 15 is 15. The LCM is the number evenly divisible by the two numbers 3 and 15. Considering the common multiples of 3 and 15, you will get to know how the least common multiple of 3 and 15 can be found. The multiples of 3 are (3, 6, 9, 12, 15, 18, ….) and the multiples of 15 are (15, 30, 45, 60, 75, ….) respectively. Division, prime factorisation and listing of the multiples are the common methods to find the LCM.
Also read: Least common multiple
What is LCM of 3 and 15?
The answer to this question is 15. The LCM of 3 and 15 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 15, is the smallest positive integer 15 which is divisible by both 3 and 15 with no remainder.
How to Find LCM of 3 and 15?
LCM of 3 and 15 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3 and 15 Using Prime Factorisation Method
The prime factorisation of 3 and 15, respectively, is given by:
3 = 3¹
15 = 3 x 5 = 3¹ x 5¹
LCM (3, 15) = 15
LCM of 3 and 15 Using Division Method
We’ll divide the numbers (3, 15) by their prime factors to get the LCM of 3 and 15 using the division method (preferably common). The LCM of 3 and 15 is calculated by multiplying these divisors.
| 3 | 3 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (3, 15) = 15
LCM of 3 and 15 Using Listing the Multiples
To calculate the LCM of 3 and 15 by listing out the common multiples, list the multiples as shown below
| Multiples of 3 | Multiples of 15 |
| 3 | 15 |
| 6 | 30 |
| 9 | 45 |
| 12 | 60 |
| 15 | 75 |
| 18 | 90 |
LCM (3, 15) = 15
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Video Lesson on Applications of LCM
LCM of 3 and 15 Solved Example
If the product of two numbers is 45, what is the LCM if the GCD is 3?
Solution:
It is given that
GCD = 3
Product of two numbers = 45
We know that
LCM x GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 45/3
LCM = 15
Hence, the LCM is 15.
Frequently Asked Questions on LCM of 3 and 15
What is the LCM of 3 and 15?
We know that
Multiples of 3 = 3, 6, 9, 12, 15, 18, ….
Multiples of 15 = 15, 30, 45, 60, 75, ….
The smallest multiple exactly divisible by 3 and 15 is 15.
If the LCM of 3 and 15 is 15, find the GCF.
LCM x GCF = 3 x 15
Given
LCM of 3 and 15 is 15
15x GCF = 45
GCF = 45/15 = 3
What are the methods used to find the LCM of 3 and 15?
The methods used to find the LCM of 3 and 15 are
Division method
Prime Factorisation
Listing the multiples
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