LCM of 6, 10 and 12 is 60. LCM depicts the least common factor or multiple of any two or more given numbers. For a strong knowledge of the LCM concept, students can refer to the article LCM with Examples formulated by subject experts in accordance with the grasping abilities of students. Taking this article as a reference, students can understand the LCM concept thoroughly. In this article, let us learn how to calculate the least common multiple of 6, 10 and 12 using solved examples and FAQs.
What is LCM of 6, 10 and 12?
The Least Common Multiple of 6, 10 and 12 is 60.
How to Find LCM of 6, 10 and 12?
LCM of 6, 10 and 12 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 6, 10 and 12 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 6, 10 and 12 are expressed as;
6 = 2 × 3
10 = 2 × 5
12 = 2 × 2 × 3
LCM (6, 10, 12) = 2 × 2 × 3 × 5 = 60
LCM of 6, 10 and 12 Using Division Method
In the division method, to find the least common multiple of 6, 10 and 12, we divide the numbers 6, 10 and 12 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 6, 10 and 12.
| 2 | 6 | 10 | 12 |
| 2 | 3 | 5 | 6 |
| 3 | 3 | 5 | 3 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (6, 10, 12) = 2 × 2 × 3 × 5 = 60
LCM of 6, 10 and 12 Using Listing the Multiples
In this method, we list down the multiples of given numbers to calculate the lowest common multiple among them. Let us have a look at the multiples of 6, 10 and 12 from the list given below:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …………
Multiples of 10: 10, 20, 30, 40, 50, 60, ………….
Multiples of 12: 12, 24, 36, 48, 60, …………..
LCM (6, 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 6, 10, 12 exactly?
Solution: The LCM of 6, 10 and 12 is the smallest number that is divisible by 6, 10, 12 exactly
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …………
Multiples of 10: 10, 20, 30, 40, 50, 60, ………….
Multiples of 12: 12, 24, 36, 48, 60, …………..
Therefore 60 is the smallest number that is divisible by 6, 10, 12 exactly.
Frequently Asked Questions on LCM of 6, 10 and 12
What is the LCM of 6, 10 and 12?
Write the LCM of 6, 10 and 12 and the HCF of 6, 10 and 12.
65 is the LCM of 6, 10 and 12. True or False.
What are the methods to find the LCM of 6, 10 and 12?
The methods used to find the LCM of 6, 10 and 12 are
Prime Factorisation
Division Method
Listing the Multiples
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