LCM of 20 and 35 is 140. By considering the multiples of 20 and 35, the number evenly divisible by 20 and 35 provides the LCM. Least common multiple of 20 and 35 is the multiple which we obtain commonly using the multiplication operation. (20, 40, 60, 80, 100, 120, ….) and (35, 70, 105, 140, 175, 210, ….) are the multiples of 20 and 35. The steps used to determine the LCM of two numbers using the methods like listing multiples, prime factorization and division are discussed here in a comprehensive manner.
Also read: Least common multiple
What is LCM of 20 and 35?
The answer to this question is 140. The LCM of 20 and 35 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 20 and 35, is the smallest positive integer 140 which is divisible by both 20 and 35 with no remainder.
How to Find LCM of 20 and 35?
LCM of 20 and 35 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 20 and 35 Using Prime Factorisation Method
The prime factorisation of 20 and 35, respectively, is given by:
20 = 2 x 2 x 5 = 2² x 5¹
35 = 5 x 7 = 5¹ x 7¹
LCM (20, 35) = 140
LCM of 20 and 35 Using Division Method
We’ll divide the numbers (20, 35) by their prime factors to get the LCM of 20 and 35 using the division method (preferably common). The LCM of 20 and 35 is calculated by multiplying these divisors.
|
2 |
20 |
35 |
|
2 |
10 |
35 |
|
5 |
5 |
35 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (20, 35) = 140
LCM of 20 and 35 Using Listing the Multiples
To calculate the LCM of 20 and 35 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 20 |
Multiples of 35 |
|
20 |
35 |
|
40 |
70 |
|
60 |
105 |
|
80 |
140 |
|
100 |
175 |
|
120 |
210 |
|
140 |
245 |
LCM (20, 35) = 140
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 20 and 35 Solved Examples
Question: The LCM and GCD of two numbers are 140 and 5 respectively. If one number is 20, what is the other?
Solution:
Consider m as the other number
GCD x LCM = 20 x m
m = (GCD x LCM)/ 20
m = (5 x 140)/20
m = 35
Hence, the other number is 35.
Frequently Asked Questions on LCM of 20 and 35
Write the methods used to determine the LCM of 20 and 35.
The methods used to determine the LCM of 20 and 35 are
Prime Factorisation
Division method
Listing the multiples
With the help of the prime factorisation method, find the LCM of 20 and 25.
First we have to know the factors to find the LCM
20 = 2 x 2 x 5 = 2² x 5¹
35 = 5 x 7 = 5¹ x 7¹
LCM is the product of prime factors raised to the highest exponent among 20 and 35.
LCM of 20 and 25 = 140
Find the GCF if the LCM of 20 and 35 is 140.
LCM x GCF = 20 x 35
As the LCM = 140
140 x GCF = 700
GCF = 700/140 = 5
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