LCM of 30, 45 and 60 is 180. LCM is the method to find the smallest possible multiple of two or more numbers. Get a good hold on the LCM concept by referring to the article LCM of Two Numbers designed by subject experts. Mastering the LCM concept will help students to solve tricky problems with ease in examinations. Here, we will learn how to find the least common multiple of 30, 45 and 60 using prime factorisation, division method and a list of multiples.
What is LCM of 30, 45 and 60?
The Least Common Multiple of 30, 45 and 60 is 180.
How to Find LCM of 30, 45 and 60?
LCM of 30, 45 and 60 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 30, 45 and 60 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 30, 45 and 60 can be expressed as;
30 = 2 × 3 × 5
45 = 3 × 3 × 5
60 = 2 × 2 × 3 × 5
LCM (30, 45, 60) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 30, 45 and 60 Using Division Method
In the division method, to calculate the least common multiple of 30, 45 and 60, we divide the numbers 30, 45 and 60 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, 45 and 60.
| 2 | 30 | 45 | 60 |
| 2 | 15 | 45 | 30 |
| 3 | 15 | 45 | 15 |
| 3 | 5 | 15 | 5 |
| 5 | 5 | 5 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (30, 45, 60) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 30, 45 and 60 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. Check the multiples of 30, 45 and 60 from the table mentioned below.
| Multiples of 30 | Multiples of 45 | Multiples of 60 |
| 30 | 45 | 60 |
| 60 | 90 | 120 |
| 90 | 135 | 180 |
| 120 | 180 | 240 |
| 150 | 225 | 300 |
| 180 | 270 | 360 |
| 210 | 315 | 420 |
| 240 | 360 | 480 |
LCM (30, 45, 60) = 180
Related Articles
Prime Factorization 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, 45, 60 exactly?
Solution: The smallest number that is divisible by 30, 45, 60 exactly is their LCM. We know that the LCM of 30, 45 and 60 is 180. Therefore the smallest number that is divisible by 30, 45, 60 exactly is 180.
Frequently Asked Questions on LCM of 30, 45 and 60
What is the LCM of 30, 45 and 60?
Is the LCM of 30, 45 and 60 the same as the HCF of 30, 45 and 60?
120 is the LCM of 30, 45 and 60. True or False.
Name the methods used to find the LCM of 30, 45 and 60.
The following methods are used to find the LCM of 30, 45 and 60
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 30, 45 and 60 using prime factorisation method.
To find the LCM using prime factorisation, we express the numbers as the product of prime factors
30 = 2 × 3 × 5
45 = 3 × 3 × 5
60 = 2 × 2 × 3 × 5
LCM (30, 45, 60) = 2 × 2 × 3 × 3 × 5 = 180
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