LCM of 8, 15 and 20 is 120. The number which is the smallest and evenly divisible among the multiples of the 8, 15 and 20 provides the LCM. By listing down the multiples of the given three numbers, the least common multiple of 8, 15 and 20 can be determined. (8, 16, 24, 32, 40, ….), (15, 30, 45, 60, 75, …..) and (20, 40, 60, 80, 100,….) are the multiples of 8, 15 and 20. The LCM of 8, 15 and 20 as per the prime factorisation method, division method and listing the multiples are provided here in a descriptive manner.
Also read: Least common multiple
What is LCM of 8, 15 and 20?
The answer to this question is 120. The LCM of 8, 15 and 20 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8, 15 and 20, is the smallest positive integer 120 which is divisible by both 8, 15 and 20 with no remainder.
How to Find LCM of 8, 15 and 20?
LCM of 8, 15 and 20 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 15 and 20 Using Prime Factorisation Method
The prime factorisation of 8, 15 and 20, respectively, is given by:
8 = 2 x 2 x 2 = 2³
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
LCM (8, 15, 20) = 120
LCM of 8, 15 and 20 Using Division Method
We’ll divide the numbers (8, 15, 20) by their prime factors to get the LCM of 8, 15 and 20 using the division method (preferably common). The LCM of 8, 15 and 20 is calculated by multiplying these divisors.
|
2 |
8 |
15 |
20 |
|
2 |
4 |
15 |
10 |
|
2 |
2 |
15 |
5 |
|
3 |
1 |
15 |
5 |
|
5 |
1 |
5 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (8, 15, 20) = 120
LCM of 8, 15 and 20 Using Listing the Multiples
To calculate the LCM of 8, 15 and 20 by listing out the common multiples, list the multiples as shown below
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, . . . .
Multiples of 20 = 20, 40, 60, 80, 100, 120, . . . .
LCM (8, 15, 20) = 120
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LCM of 8, 15 and 20 Solved Examples
Question: What is the smallest number divisible exactly by 8, 15 and 20?
Solution:
LCM is the smallest number divisible exactly by 8, 15 and 20.
Using the prime factorisation, long division and by listing the multiples, we know that the LCM of 8, 15 and 20 is 120.
Hence, the LCM is 120.
Frequently Asked Questions on LCM of 8, 15 and 20
What is the LCM of 8, 15 and 20?
List the methods which can be used to get the LCM value of 8, 15 and 20.
What is the GCF if the LCM of 8, 15 and 20 is 120?
LCM x GCF = 8 x 15 x 20
Given
LCM of 8, 15 and 20 = 120
120 x GCF = 2400
GCF = 2400/120 = 20
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