LCM of 2, 3, 4 and 5 is 60. The least common multiple denotes the smallest positive integer which is multiple in a given set of numbers. Learn the LCM concept thoroughly by using the article Least Common Multiple (LCM) which is prepared with the utmost care by the expert faculty. This article explains the LCM concept in a comprehensive manner to provide the best reference material for study purposes. In this article, let us learn the simple method of how to find the least common multiple of 2, 3, 4 and 5.
What is LCM of 2, 3, 4 and 5?
The Least Common Multiple of 2, 3, 4 and 5 is 60.
How to Find LCM of 2, 3, 4 and 5?
The LCM of 2, 3, 4 and 5 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 2, 3, 4 and 5 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 2, 3, 4 and 5 can be expressed as;
2 = 2
3 = 3
4 = 2 × 2
5 = 5
LCM (2, 3, 4, 5) = 2 × 2 × 3 × 5 = 60
LCM of 2, 3, 4 and 5 Using Division Method
In the division method, we divide the numbers 2, 3, 4 and 5 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 2, 3, 4 and 5.
| 2 | 2 | 3 | 4 | 5 |
| 2 | 1 | 3 | 2 | 5 |
| 3 | 1 | 3 | 1 | 5 |
| 5 | 1 | 1 | 1 | 5 |
| x | 1 | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (2, 3, 4, 5) = 2 × 2 × 3 × 5 = 60
LCM of 2, 3, 4 and 5 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. A few multiples of 2, 3, 4 and 5 are as follows:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ………, 56, 58, 60, …….
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ……, 54, 57, 60, ……..
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …………, 52, 56, 60, …….
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, …..
LCM (2, 3, 4, 5) = 60
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 2, 3, 4, 5 exactly?
Solution: The smallest number that is divisible by 2, 3, 4, 5 exactly is 60. The LCM of 2, 3, 4 and 5 is 60. Therefore the smallest number that is divisible by 2, 3, 4, 5 exactly is 60.
Frequently Asked Questions on LCM of 2, 3, 4 and 5
What is the LCM of 2, 3, 4 and 5?
Is the LCM of 2, 3, 4 and 5 the same as the HCF of 2, 3, 4 and 5?
What are the methods used to find the LCM of 2, 3, 4 and 5?
The following methods are used to find the LCM of 2, 3, 4 and 5
Prime Factorisation
Division method
Listing of Multiples
Using prime factorisation, find the LCM of 2, 3, 4 and 5.
In prime factorisation, we express the numbers as the product of prime factors to find the LCM
2 = 2
3 = 3
4 = 2 × 2
5 = 5
LCM (2, 3, 4, 5) = 2 × 2 × 3 × 5 = 60
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