LCM of 4, 10 and 12 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) explains the LCM concept in an easy to understand format. Using this article while solving problems provides an extra edge and boosts confidence among students during final examinations. Here, we will learn how to verify the least common multiple of 4, 10 and 12 in an efficient way.
What is LCM of 4, 10 and 12?
The Least Common Multiple of 4, 10 and 12 is 60.
How to Find LCM of 4, 10 and 12?
The LCM of 4, 10 and 12 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 4, 10 and 12 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 4, 10 and 12 can be expressed as;
4 = 2 × 2
10 = 2 × 5
12 = 2 × 2 × 3
LCM (4, 10, 12) = 2 × 2 × 3 × 5 = 60
LCM of 4, 10 and 12 Using Division Method
In the division method, we divide the numbers 4, 10 and 12 by a common prime number until the remainder is a prime number or one. The product of these divisors gives the least common multiple of 4, 10 and 12.
| 2 | 4 | 10 | 12 |
| 2 | 2 | 5 | 6 |
| 3 | 1 | 5 | 3 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (4, 10, 12) = 2 × 2 × 3 × 5 = 60
LCM of 4, 10 and 12 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The multiples of 4, 10 and 12 are as follows:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ………., 52, 56, 60, ……..
Multiples of 10: 10, 20, 30, 40, 50, 60, …….
Multiples of 12: 12, 24, 36, 48, 60, …….
LCM (4, 10, 12) = 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, 10, 12 exactly?
Solution: The smallest number that is divisible by 4, 10,12 exactly is their LCM. The LCM of 4, 10 and 12 is 60. Hence the smallest that is divisible by 4, 10, 12 exactly is 60.
Frequently Asked Questions on LCM of 4, 10 and 12
What is the LCM of 4, 10 and 12?
Is the LCM of 4, 10 and 12 and the HCF of 4, 10 and 12 are same?
What are the methods used to find the LCM of 4, 10 and 12?
The methods used to find the LCM of 4, 10 and 12 are as follows:
Prime Factorisation
Division method
Listing of Multiples
Determine the LCM of 4, 10 and 12 using prime factorisation.
In prime factorisation, we express the given numbers as the product of prime factors to determine their LCM
4 = 2 × 2
10 = 2 × 5
12 = 2 × 2 × 3
LCM (4, 10, 12) = 2 × 2 × 3 × 5 = 60
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