LCM of 4, 6 and 10 is 60. LCM denotes the smallest positive number that is a multiple of two or more numbers. Students can solve the problems of LCM with ease using the article Least Common Multiple (LCM) prepared by experts in simple language. This article is the best material for students to obtain better conceptual knowledge and also build skills vital from an exam perspective. In this article, let us learn how to determine the least common multiple of 4, 6 and 10 in a detailed manner.
What is LCM of 4, 6 and 10?
The Least Common Multiple of 4, 6 and 10 is 60.
How to Find LCM of 4, 6 and 10?
LCM of 4, 6 and 10 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 4, 6 and 10 Using Prime Factorisation Method
In the prime factorisation method, LCM of 4, 6 and 10 can be obtained by multiplying prime factors raised to their respective highest power.
4 = 2 × 2
6 = 2 × 3
10 = 2 × 5
LCM (4, 6, 10) = 2 × 2 × 3 × 5 = 60
LCM of 4, 6 and 10 Using Division Method
In the division method, to find the LCM, we divide the numbers 4, 6 and 10 by their prime factors until we get the result as one in the complete row. The product of these divisors indicates the least common multiple of 4, 6 and 10.
| 2 | 4 | 6 | 10 |
| 2 | 2 | 3 | 5 |
| 3 | 1 | 3 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (4, 6, 10) = 2 × 2 × 3 × 5 = 60
LCM of 4, 6 and 10 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the least common multiple among them. The multiples of 4, 6 and 10 are as follows:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ………
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …………
Multiples of 10: 10, 20, 30, 40, 50, 60, …………….
LCM (4, 6, 10) = 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 4, 6, 10 exactly?
Solution: The smallest number that is divisible by 4, 6,10 exactly is their LCM. The LCM of 4, 6 and 10 is 60. Hence the smallest number that is divisible by 4, 6, 10 exactly is 60.
Frequently Asked Questions on LCM of 4, 6 and 10
What is the LCM of 4, 6 and 10?
Is the LCM of 4, 6 and 10 the same as the HCF of 4, 6 and 10?
Mention the methods used to find the least common multiple of 4, 6 and 10.
The methods used to find the least common multiple of 4, 6 and 10 are as follows:
Prime Factorisation
Division method
Listing the Multiples
How to find the LCM of 4, 6 and 10 using prime factorisation?
To find the LCM using prime factorisation, we write the numbers as the product of prime factors
4 = 2 × 2
6 = 2 × 3
10 = 2 × 5
LCM (4, 6, 10) = 2 × 2 × 3 × 5 = 60
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