LCM of 4, 5 and 6 is 60. The least common multiple denotes the smallest positive integer which is multiple in a given set of numbers. The article Least Common Multiple (LCM) has been designed by experts with the aim to provide the best reference guide to obtain the proper knowledge of the LCM concept. This will also help students solve the problems relying on the LCM with speed and accuracy. Let us learn how to verify the least common multiple of 4, 5 and 6 in a detailed manner in this article.
What is LCM of 4, 5 and 6?
The Least Common Multiple of 4, 5 and 6 is 60.
How to Find LCM of 4, 5 and 6?
LCM of 4, 5 and 6 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 4, 5 and 6 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. Hence the numbers 4, 5 and 6 can be expressed as;
4 = 2 × 2
5 = 5
6 = 2 × 3
LCM (4, 5, 6) = 2 × 2 × 3 × 5 = 60
LCM of 4, 5 and 6 Using Division Method
In this method, we divide the numbers 4, 5 and 6 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 4, 5 and 6.
| 2 | 4 | 5 | 6 |
| 2 | 2 | 5 | 3 |
| 3 | 1 | 5 | 3 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No more further division can be done.
Hence, LCM (4, 5, 6) = 2 × 2 × 3 × 5 = 60
LCM of 4, 5 and 6 Using Listing the Multiples
Here, the multiples of each number are listed until the first common multiple is found. Let us have a look at the multiples of 4, 5 and 6 mentioned below.
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, ………..
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ……..
LCM (4, 5, 6) = 60
Related Articles
Prime Factorisation 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 4, 5, 6 exactly?
Solution: 60 is the smallest number that is divisible by 4, 5, 6 exactly.
2. What is the lowest common multiple of 4, 5 and 6?
Solution: The lowest common multiple of 4, 5 and 6 is 60.
Frequently Asked Questions on LCM of 4, 5 and 6
What is the LCM of 4, 5 and 6?
What are the methods used to find the LCM of 4, 5 and 6?
The methods used to find the LCM of 4, 5 and 6 are as follows:
Prime Factorisation
Division Method
Listing the Multiples
What is the LCM of 4, 5 and 6 and the GCF of 4, 5 and 6?
Write the relation between GCF and LCM of 4, 5 and 6.
The relation between GCF and LCM of 4, 5 and 6 is
GCF × LCM = 4 × 5 × 6
GCF × LCM =120
How to find the LCM of 4, 5 and 6 using the prime factorisation method?
Here, we express the numbers as the product of prime factors to find the LCM
4 = 2 × 2
5 = 5
6 = 2 × 3
LCM (4, 5, 6) = 2 × 2 × 3 × 5 = 60
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