LCM of 30, 36 and 40 is 360. The LCM is the method to find the least common multiple between any two or more numbers. Students who wish to obtain a thorough understanding of the LCM concept are advised to follow the article LCM with Examples anytime as per their needs. Using this article while solving the problems creates interest in learning the concepts among students. Here, we will discuss how to find the least common multiple of 30, 36, and 40 with a complete explanation.
What is LCM of 30, 36 and 40?
The Least Common Multiple of 30, 36 and 40 is 360.
How to Find LCM of 30, 36 and 40?
LCM of 30, 36 and 40 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 30, 36 and 40 Using Prime Factorisation Method
In the prime factorisation method, LCM of 30, 36 and 40 can be obtained by multiplying prime factors raised to their respective highest power.
30 = 2 × 3 × 5
36 = 2 × 2 × 3 × 3
40 = 2 × 2 × 2 × 5
LCM (30, 36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 30, 36 and 40 Using Division Method
In the division method, to determine the least common multiple of 30, 36, and 40, we divide the numbers 30, 36 and 40 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 30, 36, and 40.
| 2 | 30 | 36 | 40 |
| 2 | 15 | 18 | 20 |
| 2 | 15 | 9 | 10 |
| 3 | 15 | 9 | 5 |
| 3 | 5 | 3 | 5 |
| 5 | 5 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (30, 36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 30, 36 and 40 Using Listing the Multiples
In this method, we list down the multiples of 30, 36, and 40 to find the least common multiple among them. The multiples of 30, 36, and 40 are shown below.
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, ………..
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, ……….
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, ………….
LCM (30, 36, 40) = 360
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 30, 36, 40 exactly?
Solution: The smallest number that is divisible by 30, 36, 40 exactly is their LCM. Here the LCM of 30, 36 and 40 is 360. Hence the smallest number that is divisible by 30, 36, 40 exactly is 360.
Frequently Asked Questions on LCM of 30, 36 and 40
What is the LCM of 30, 36 and 40?
Is the LCM of 30, 36 and 40 the same as the HCF of 30, 36 and 40?
460 is the LCM of 30, 36 and 40. True or False.
What are the methods used to find the LCM of 30, 36 and 40?
The methods used to find the LCM of 30, 36 and 40 are
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 30, 36 and 40 using prime factorisation.
In this method, we write the numbers as the product of prime factors to verify the LCM
30 = 2 × 3 × 5
36 = 2 × 2 × 3 × 3
40 = 2 × 2 × 2 × 5
LCM (30, 36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
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