LCM of 20, 40 and 60 is 120. LCM can be defined as the smallest common multiple of two or more numbers. Students must possess a thorough knowledge of the LCM concept as it would be continued in further education levels. Least Common Multiple (LCM) is the perfect study guide for obtaining proficiency in the LCM concept. In this article, let us learn in detail how to verify the least common multiple of 20, 40 and 60 with a complete explanation.
What is LCM of 20, 40 and 60?
The Least Common Multiple of 20, 40 and 60 is 120.
How to Find LCM of 20, 40 and 60?
LCM of 20, 40 and 60 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 20, 40 and 60 Using Prime Factorisation Method
In the prime factorisation method, 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.
20 = 2 × 2 × 5
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
LCM (20, 40, 60) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 20, 40 and 60 Using Division Method
In the division method, to determine the least common multiple of 20, 40 and 60, we divide the numbers 20, 40 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 20, 40 and 60.
| 2 | 20 | 40 | 60 |
| 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 (20, 40, 60) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 20, 40 and 60 Using Listing the Multiples
In this method, we list the multiples of 20, 40 and 60 to find the least common multiple among them. Let us glance at the multiples of 20, 40 and 60 from the table given below.
| Multiples of 20 | Multiples of 40 | Multiples of 60 |
| 20 | 40 | 60 |
| 40 | 80 | 120 |
| 60 | 120 | 180 |
| 80 | 160 | 240 |
| 100 | 200 | 300 |
| 120 | 240 | 360 |
| 140 | 280 | 420 |
LCM (20, 40, 60) = 120
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 20, 40, 60 exactly?
Solution: The smallest number that is divisible by 20, 40, 60 exactly is their LCM. We know that the LCM of 20, 40 and 60 is 120. Thus the smallest number that is divisible by 20, 40, 60 exactly is 120.
Frequently Asked Questions on LCM of 20, 40 and 60
What is the LCM of 20, 40 and 60?
Is the LCM of 20, 40 and 60 the same as the HCF of 20, 40 and 60?
Name the methods used to find the least common multiple of 20, 40 and 60.
The methods used to find the least common multiple of 20, 40 and 60 are:
Prime Factorisation
Division method
Listing the Multiples
Find the LCM of 20, 40 and 60 using the prime factorisation method.
In the prime factorisation, we write the numbers as the product of prime factors to find the LCM
20 = 2 × 2 × 5
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
LCM (20, 40, 60) = 2 × 2 × 2 × 3 × 5 = 120
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