LCM of 15 and 35 is 105. The smallest number evenly divisible among the multiples of the two numbers shows the LCM. By analyzing the common multiples, the least common multiple of 15 and 35 can be found. (15, 30, 45, 60, 75, 90, 105, 120, ….) and (35, 70, 105, 140, 175,….) are the multiples of 15 and 35. The LCM of the given numbers can be determined using methods like prime factorisation, division method and by listing out the multiples.
Also read: Least common multiple
What is LCM of 15 and 35?
The answer to this question is 105. The LCM of 15 and 35 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 15 and 35, is the smallest positive integer 105 which is divisible by both 15 and 35 with no remainder.
How to Find LCM of 15 and 35?
LCM of 15 and 35 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 35 Using Prime Factorisation Method
The prime factorisation of 15 and 35, respectively, is given by:
15 = 3 x 5 = 3¹ x 5¹
35 = 5 x 7 = 5¹ x 7¹
LCM (15, 35) = 105
LCM of 15 and 35 Using Division Method
We’ll divide the numbers (15, 35) by their prime factors to get the LCM of 15 and 35 using the division method (preferably common). The LCM of 15 and 35 is calculated by multiplying these divisors.
| 3 | 15 | 35 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (15, 35) = 105
LCM of 15 and 35 Using Listing the Multiples
To calculate the LCM of 15 and 35 by listing out the common multiples, list the multiples as shown below
| Multiples of 15 | Multiples of 35 |
| 15 | 35 |
| 30 | 70 |
| 45 | 105 |
| 60 | 140 |
| 75 | 175 |
| 90 | – |
| 105 | – |
| 120 | – |
LCM (15, 35) = 105
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Video Lesson on Applications of LCM
LCM of 15 and 35 Solved Example
Question: If the GCD is 5 and the product of two numbers is 525, what is the LCM?
Solution:
It is given that;
Product of two numbers = 525
GCD = 5
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 525/5
LCM = 105
Hence, the LCM is 105.
Frequently Asked Questions on LCM of 15 and 35
What is the LCM of 15 and 35?
The LCM of 15 and 35 is 105.
The smallest multiple exactly divisible by 15 and 35 should be found.
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, …
Multiples of 35 = 35, 70, 105, 140, 175, 210, ….
The smallest common multiple exactly divisible by 15 and 35 is 105.
List the methods used to find the LCM of 15 and 35.
What is the GCF if the LCM of 15 and 35 is 105?
LCM x GCF = 15 x 35
Given
LCM of 15 and 35 = 105
105 x GCF = 525
GCF = 525/105 = 5
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