LCM of 21 and 42 is 42. Learn how the LCM of 21 and 42 can be calculated by using this article. The least common multiple of 21 and 42 is the smallest number evenly divisible by the given numbers. The multiples of 21 are (21, 42, 63, 84, 105, 126, ….) and the multiples of 42 are (42, 84, 126, 168, ….) respectively. Division, Prime factorisation and listing of the multiples are the methods used to find the LCM.
Also read: Least common multiple
What is LCM of 21 and 42?
The answer to this question is 42. The LCM of 21 and 42 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 21 and 42, is the smallest positive integer 42 which is divisible by both 21 and 42 with no remainder.
How to Find LCM of 21 and 42?
LCM of 21 and 42 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21 and 42 Using Prime Factorisation Method
The prime factorisation of 21 and 42, respectively, is given by:
21 = 3 x 7 = 3¹ x 7¹
42 = 2 x 3 x 7 = 2¹ x 3¹ x 7¹
LCM (21, 42) = 42
LCM of 21 and 42 Using Division Method
We’ll divide the numbers (21, 42) by their prime factors to get the LCM of 21 and 42 using the division method (preferably common). The LCM of 21 and 42 is calculated by multiplying these divisors.
|
3 |
21 |
42 |
|
2 |
7 |
14 |
|
7 |
7 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (21, 42) = 42
LCM of 21 and 42 Using Listing the Multiples
To calculate the LCM of 21 and 42 by listing out the common multiples, list the multiples as shown below
|
Multiples of 21 |
Multiples of 42 |
|
21 |
42 |
|
42 |
84 |
|
63 |
126 |
|
84 |
168 |
|
105 |
210 |
|
126 |
252 |
LCM (21, 42) = 42
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Video Lesson on Applications of LCM
LCM of 21 and 42 Solved Examples
Question: If the product of two numbers is 882, calculate the LCM if the GCD is 21.
Solution:
It is given that,
GCD = 21
Product of two numbers = 882
We know that;
LCM x GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 882/21
LCM = 42
Hence, the LCM is 42.
Frequently Asked Questions on LCM of 21 and 42
What is the LCM of 21 and 42?
We know that
(21, 42, 63, 84, ….) are the multiples of 21
(42, 84, 126, 168, ….) are the multiples of 42
The smallest multiple exactly divisible by 21 and 42 is 42.
If the LCM of 21 and 42 is 42, determine the GCF.
LCM x GCF = 21 x 42
Given
LCM of 21 and 42 is 42
42 x GCF = 882
GCF = 882/42 = 21
What are the methods used to find the LCM of 21 and 42?
The methods used to find the LCM of 21 and 42 are:
Division method
Prime Factorisation
Listing the multiples
The LCM and GCD of two numbers are 42 and 21. If one number is 21, determine the other.
Consider x as the other number.
GCD x LCM = 21 x x
x = (GCD x LCM)/ 21
x = (21 x 42)/21
x = 42
Hence, the other number is 42.
What is the relation between LCM and GCF of 21 and 42?
The relation between LCM and GCF of 21 and 42 is
LCM x GCF = 21 x 42
LCM x GCF = 882
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