LCM of 15 and 17 is 72. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. LCM of 15 and 17 is the smallest number among all common multiples of 15 and 17. The first few multiples of 15 and 17 are (15, 30, 45, 60, 75, . . . ) and (17, 34, 51, 68, 85, 102, 119, . . . ) respectively.
Also read: Least common multiple
What is LCM of 15 and 17?
The answer to this question is 255. The LCM of 15 and 17 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 15 and 17, is the smallest positive integer 255 which is divisible by both 15 and 17 with no remainder.
How to Find LCM of 15 and 17?
LCM of 15 and 17 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 17 Using Prime Factorisation Method
The prime factorisation of 15 and 17, respectively, is given by:
(3 × 5) = 31 × 51 and (17) = 171
LCM (15, 17) = 140
LCM of 15 and 17 Using Division Method
We’ll divide the numbers (15, 17) by their prime factors to get the LCM of 15 and 17 using the division method (preferably common). The LCM of 15 and 17 is calculated by multiplying these divisors.
| 3 | 15 | 17 |
| 5 | 5 | 17 |
| 17 | 1 | 17 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (15, 17) = 255
LCM of 15 and 17 Using Listing the Multiples
To calculate the LCM of 15 and 17 by listing out the common multiples, list the multiples as shown below
| Multiples of 15 | Multiples of 17 |
| 15 | 17 |
| 30 | 34 |
| 45 | 51 |
| ….. | …. |
| 255 | 255 |
The smallest common multiple of 15 and 17 is 255.
Therefore LCM (15, 17) = 255
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LCM of 15 and 17 Solved Example
Question: The product of two numbers is 255. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 255
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 255/1
Therefore, the LCM is 255.
The probable combination for the given case is LCM(15, 17) = 255.
Frequently Asked Questions on LCM of 15 and 17
What is the LCM of 15 and 17?
List the methods used to find the LCM of 15 and 17.
Which of the following is the LCM of 15 and 17? 255, 24, 42, 21
What is the Relation Between GCF and LCM of 15, 17?
If the LCM of 17 and 15 is 255, Find its GCF.
Since the LCM of 17 and 15 = 255
⇒ 255 × GCF(17, 15) = 255
Therefore, the GCF (greatest common factor) = 255/255 = 1.
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