LCM of 10, 20 and 30 is 60. LCM denotes the smallest positive number which is a multiple of two or more numbers. Expert faculty have carefully drafted the article LCM with Examples to provide students with the perfect guide to solve tricky questions effortlessly. The first step towards achieving success in exams is to have a firm grip on the LCM concept. Let us learn how to verify the least common multiple of 10, 20, and 30 with the help of solved examples and FAQs in an efficient manner here.
What is LCM of 10, 20 and 30?
The answer to this question is 60.
How to Find LCM of 10, 20 and 30?
LCM of 10, 20 and 30 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 10, 20 and 30 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 10, 20 and 30 can be expressed as;
10 = 2 × 5
20 = 2 × 2 × 5
30 = 2 × 3 × 5
LCM (10, 20, 30) = 2 × 2 × 3 × 5 = 60
LCM of 10, 20 and 30 Using Division Method
In this method, we divide the numbers 10, 20 and 30 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 10, 20 and 30.
| 2 | 10 | 20 | 30 |
| 2 | 5 | 10 | 15 |
| 3 | 5 | 5 | 15 |
| 5 | 5 | 5 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (10, 20, 30) = 2 × 2 × 3 × 5 = 60
LCM of 10, 20 and 30 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 10, 20, and 30.
| Multiples of 10 | Multiples of 20 | Multiples of 30 |
| 10 | 20 | 30 |
| 20 | 40 | 60 |
| 30 | 60 | 90 |
| 40 | 80 | 120 |
| 50 | 100 | 150 |
| 60 | 120 | 180 |
LCM (10, 20, 30) = 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 10, 20, 30 exactly?
Solution: The smallest number that is divisible by 10, 20, 30 exactly is their LCM. The LCM of 10, 20 and 30 is 60. Hence 60 is the smallest number that is divisible by 10, 20, 30 exactly.
Frequently Asked Questions on LCM of 10, 20 and 30
What is the LCM of 10, 20 and 30?
Mention the LCM of 10, 20 and 30 and the HCF of 10, 20 and 30.
How do you find the LCM of 10, 20 and 30 by the prime factorisation method?
In this method, the given natural numbers are expressed as the product of prime factors.
10 = 2 × 5
20 = 2 × 2 × 5
30 = 2 × 3 × 5
LCM (10, 20, 30) = 2 × 2 × 3 × 5 = 60
What are the methods used to find the LCM of 10, 20 and 30?
The following methods can be used to find the LCM of 10, 20 and 30
Prime Factorisation
Division Method
Listing the Multiples
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