LCM of 8 and 15 is 120. The method to find the smallest possible multiple of two or more numbers is known as Least Common Multiple. Follow the Least Common Multiple (LCM) to master the concept of LCM. Prime factorisation, division method and listing multiples are the three methods that can be used to find the LCM of two or more numbers. In this article, we will learn how to find the least common multiple of 8 and 15 in a precise manner.
What is LCM of 8 and 15?
The answer to this question is 120.
How to Find LCM of 8 and 15?
LCM of 8 and 15 can be determined by using the methods presented below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 15 Using Prime Factorisation Method
The least common multiple of 8 and 15 using the prime factorisation method can be calculated by multiplying prime factors raised to their respective highest power. This can be done as below.
8 = 2 × 2 × 2
15 = 3 × 5
LCM (8, 15) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 8 and 15 Using Division Method
In the division method, to determine the LCM of 8 and 15, we divide the numbers 8 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 8 and 15.
| 2 | 8 | 15 |
| 2 | 4 | 15 |
| 2 | 2 | 15 |
| 3 | 1 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (8, 15) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 8 and 15 Using Listing the Multiples
We list out the multiple of 8 and 15 to determine the least common multiple of 8 and 15 in this method. The multiples of 8 and 15are given below.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ………,, 104, 112, 120, ………
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, …………
LCM (8, 15) = 120
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: The GCD and LCM of two numbers are 1 and 120. If one number is 8, calculate the other number.
Solution: Let the other number be m
We know that,
GCD × LCM = 8 × m
m = (GCD × LCM)/8
m = (1 × 120)/8
m = 15
Hence the other number is 15.
Q. 2: What is the smallest number that is divisible by both 8 and 15?
Solution: 120 is the smallest number that is divisible by both 8 and 15.
Frequently Asked Questions on LCM of 8 and 15
What is the LCM of 8 and 15?
Is the LCM of 8 and 15 the same as the HCF of 8 and 15?
What are the common prime factors of 8 and 15?
List the methods used to find the LCM of 8 and 15.
The following methods are used to find the LCM of 8 and 15
Prime Factorisation
Division Method
Listing the Multiples
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