LCM of 15 and 75 is 75. The LCM concept is mainly used to make the simplification process easier. The article Least Common Multiple (LCM) prepared by experts in a simple format, helps students to understand the LCM concept effortlessly. Practising the problem by referring to this article on a regular basis enables students to secure excellent marks in final exams. In this article, let us grasp the simple process of representing the least common multiple of 15 and 75.
What is LCM of 15 and 75?
The answer to this question is 75.
How to Find LCM of 15 and 75?
The LCM of 15 and 75 can be determined by using the methods given below:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 15 and 75 Using Prime Factorisation Method
The prime factorisation method is one of the most common ways of calculating LCM. To find the LCM of 15 and 75, we use the steps as follows:
15 = 3 × 5
75 = 3 × 5 × 5
LCM (15, 75) = 3 × 5 × 5 = 75
LCM of 15 and 75 Using Division Method
In the division method, to determine the least common multiple of 15 and 75, we divide the numbers 15 and 75 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 15 and 75.
| 3 | 15 | 75 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (15, 75) = 3 × 5 × 5 = 75
LCM of 15 and 75 Using Listing the Multiples
In this method, we list out the multiples of given numbers to find the least common multiple among them. The following table shows the multiples of 15 and 75.
| Multiples of 15 | Multiples of 75 |
| 15 | 75 |
| 30 | 150 |
| 45 | 225 |
| 60 | 300 |
| 75 | 375 |
| 90 | 450 |
LCM (15, 75) = 75
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 15 and 75?
Solution: 75 is the smallest number that is divisible by both 15 and 75.
2. The GCD and LCM of the two numbers are 15 and 75. If one number is 75. What is the other number?
Solution: Let the other number be k
We know that
GCD × LCM = 75 × k
k = (GCD × LCM)/75
k = (15 × 75)/75
k = 15
Hence the other number is 15.
Frequently Asked Questions on LCM of 15 and 75
What is the LCM of 15 and 75?
Write the LCM of 15 and 75 and the HCF of 15 and 75.
Is 85 the LCM of 15 and 75?
What are the methods used to determine the LCM of 15 and 75?
The following methods are used to determine the LCM of 15 and 75
Prime Factorisation
Division Method
Listing the Multiples
Calculate the GCF if the LCM of 15 and 75 is 75.
GCF × LCM = 15 × 75
Given
GCF × 75 = 15 × 75
GCF = 15
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