LCM of 30, 40 and 60 is 120. LCM denotes the least common factor or multiple of any two or more given numbers. Students can make use of the article developed by the experts to erase the doubts based on the LCM concept immediately. The article Lowest Common Multiple (LCM) in simple language helps students to speed up their problem-solving and time management skills which are crucial for an excellent score in exams. Here, let us grasp the simple method of finding the least common multiple of 30, 40 and 60 in detail.
What is LCM of 30, 40 and 60?
The Least Common Multiple of 30, 40 and 60 is 120.
How to Find LCM of 30, 40 and 60?
LCM of 30, 40 and 60 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 30, 40 and 60 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 30, 40, and 60 are expressed as;
30 = 2 × 3 × 5
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
LCM (30, 40, 60) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 30, 40 and 60 Using Division Method
In the division method, to find the least common multiple of 30, 40 and 60, we divide the numbers 30, 40 and 60 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 30, 40 and 60.
| 2 | 30 | 40 | 60 |
| 2 | 15 | 20 | 30 |
| 2 | 15 | 10 | 15 |
| 3 | 15 | 5 | 15 |
| 5 | 5 | 5 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (30, 40, 60) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 30, 40 and 60 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. Check the multiples of 30, 40 and 60 from the table given below.
| Multiples of 30 | Multiples of 40 | Multiples of 60 |
| 30 | 40 | 60 |
| 60 | 80 | 120 |
| 90 | 120 | 180 |
| 120 | 160 | 240 |
| 150 | 200 | 300 |
LCM (30, 40, 60) = 120
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, 40, 60 exactly?
Solution: The smallest number that is divisible by 30, 40, 60 exactly is their LCM. The LCM of 30, 40 and 60 is 120. Therefore, the smallest number that is divisible by 30, 40, 60 exactly is 120.
Frequently Asked Questions on LCM of 30, 40 and 60
What is the LCM of 30, 40 and 60?
Is the LCM of 30, 40 and 60 and the HCF of 30, 40, and 60 are same?
Name the methods used to find the LCM of 30, 40 and 60.
The methods used to find the LCM of 30, 40 and 60 are as follows:
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 30, 40 and 60 using prime factorisation.
Here, we express the given numbers as the product of prime factors to find their LCM
30 = 2 × 3 × 5
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
LCM (30, 40, 60) = 2 × 2 × 2 × 3 × 5 = 120
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