LCM of 3, 5 and 8 is 120. LCM is the smallest common multiple of two or more numbers. For in-depth knowledge of the LCM concept, experts designed the article Least Common Multiple (LCM) in simple language for students. Regular use of this article enables students to solve difficult problems based on the LCM concept with speed and correctness. This article explains the simple process of finding the least common multiple of 3, 5 and 8 with the help of solved examples and FAQs.
What is LCM of 3, 5 and 8?
The Least Common Multiple of 3, 5 and 8 is 120.
How to Find LCM of 3, 5 and 8?
The LCM of 3, 5 and 8 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 3, 5 and 8 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 3, 5 and 8 can be represented as;
3 = 3
5 = 5
8 = 2 × 2 × 2
LCM (3, 5, 8) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 3, 5 and 8 Using Division Method
In the division method, we divide the numbers 3, 5 and 8 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 3, 5 and 8.
| 2 | 3 | 5 | 8 |
| 2 | 3 | 5 | 4 |
| 2 | 3 | 5 | 2 |
| 3 | 3 | 5 | 1 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Therefore, LCM (3, 5, 8) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 3, 5 and 8 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 3, 5 and 8 are as follows:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, …….., 114, 117, 120, ……..
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ……, 110, 115, 120, ……
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ….., 88, 96, 104, 112, 120,……
LCM (3, 5, 8) = 120
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 3, 5, 8 exactly?
Solution: 120 is the smallest number that is divisible by 3, 5, 8 exactly.
2. What is the least common factor of 3, 5, 8 and 10?
Solution: 120 is the least common factor of 3, 5, 8 and 10.
Frequently Asked Questions on LCM of 3, 5 and 8
What is the LCM of 3, 5 and 8?
What are the methods used to find the LCM of 3, 5 and 8?
The following methods are used to find the LCM of 3, 5 and 8:
Prime Factorisation
Division Method
Listing the Multiples
Using prime factorisation, find the LCM of 3, 5 and 8.
We write the numbers as the product of prime factors to verify the LCM using prime factorisation
3 = 3
5 = 5
8 = 2 × 2 × 2
LCM (3, 5, 8) = 2 × 2 × 2 × 3 × 5 = 120
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