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You have reached us maybe looking for answers to the questions like: What is the greatest common factor of 20 and 35? or what is the highest common factor (HCF) of 20 and 35?
What is the GCF of 20 and 35?
The first step to find the gcf of 20 and 35 is to list the factors of each number. The factors of 20 are 1, 2, 4, 5, 10 and 20. The factors of 35 are 1, 5, 7 and 35. So, the Greatest Common Factor for these numbers is 5 because it divides all them without a remainder. Read more about Common Factors below.
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The first step is to find all divisors of each number. For instance, let us find the gcf(20, 35).
In this case we have:
- The factors of 20 (all the whole numbers that can divide the number without a remainder) are 1, 2, 4, 5, 10 and 20;
- The factors of 35 are 1, 5, 7 and 35.
The second step is to analyze which are the common divisors. It is not difficult to see that the 'Greatest Common Factor' or 'Divisor' for 20 and 35 is 5. The GCF is the largest common positive integer that divides all the numbers (20, 35) without a remainder.
In the name greatest common divisor, the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), greatest common measure, among others.
So, the GCF is also known as:
- Greatest common divisor (gcd);
- Highest common factor (hcf);
- Greatest common measure (gcm), or
- Highest common divisor
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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
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.
The methods used to determine the LCM of 20 and 35 are
Prime Factorisation
Division method
Listing the multiples
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
LCM x GCF = 20 x 35
As the LCM = 140
140 x GCF = 700
GCF = 700/140 = 5
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 20 and 35 is 140.
LCM(20,35) = 140
Least Common Multiple of 20 and 35 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20 and 35, than apply into the LCM equation.
GCF(20,35) = 5 LCM(20,35) = ( 20 × 35) / 5 LCM(20,35) = 700 / 5
LCM(20,35) = 140
Least Common Multiple (LCM) of 20 and 35 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 20 and 35. First we will calculate the prime factors of 20 and 35.
Prime Factorization of 20
Prime factors of 20 are 2, 5. Prime factorization of 20 in exponential form is:
20 = 22 × 51
Prime Factorization of 35
Prime factors of 35 are 5, 7. Prime factorization of 35 in exponential form is:
35 = 51 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 20 and 35.
LCM(20,35) = 22 × 51 × 71
LCM(20,35) = 140
The LCM of 20 and 35 is 140.
Steps to find LCM
- Find the prime factorization of 20
20 = 2 × 2 × 5 - Find the prime factorization of 35
35 = 5 × 7 - Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 2 × 5 × 7
- LCM = 140
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Find least common multiple (LCM) of: 40 & 70 60 & 105 100 & 175 4 & 7 140 & 245 40 & 35 20 & 70 60 & 35 20 & 105 100 & 35 20 & 175 140 & 35 20 & 245
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