LCM of 4 and 21 is 84. The common multiple divisible by the given two numbers is the LCM value. Least common multiple of 4 and 21 is the smallest number we obtain from the common multiples. (4, 8, 12, 16, 20, 24, ….) and (21, 42, 63, 84, 105, 126,….) are the first few multiples of 4 and 21. Few methods such as division, prime factorisation and listing of multiples are used to get the LCM.
Also read: Least common multiple
What is LCM of 4 and 21?
The answer to this question is 84. The LCM of 4 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4 and 21, is the smallest positive integer 84 which is divisible by both 4 and 21 with no remainder.
How to Find LCM of 4 and 21?
LCM of 4 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4 and 21 Using Prime Factorisation Method
The prime factorisation of 4 and 21, respectively, is given by:
4 = 2 x 2 = 2²
21 = 3 x 7 = 3¹ x 7¹
LCM (4, 21) = 84
LCM of 4 and 21 Using Division Method
We’ll divide the numbers (4, 21) by their prime factors to get the LCM of 4 and 21 using the division method (preferably common). The LCM of 4 and 21 is calculated by multiplying these divisors.
|
2 |
4 |
21 |
|
2 |
2 |
21 |
|
3 |
1 |
21 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (4, 21) = 84
LCM of 4 and 21 Using Listing the Multiples
To calculate the LCM of 4 and 21 by listing out the common multiples, list the multiples as shown below
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 68, 72, 76, 80, 84, . . . .
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . ., 21, 42, 63, 84, . . . .
LCM (4, 21) = 84
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LCM of 4 and 21 Solved Examples
Question: The LCM and GCD of two numbers are 84 and 1 respectively. If one of the numbers is 21, find the other.
Solution:
Consider a as the other number.
GCD x LCM = 21 x a
a = (GCD x LCM)/ 21
a = (1 x 84)/21
a = 4
Hence, the other number is 4.
Frequently Asked Questions on LCM of 4 and 21
Find the LCM of 4 and 21.
Which methods can be used to find the LCM of 4 and 21?
Calculate the GCF if the LCM of 4 and 21 is 84.
LCM x GCF = 4 x 21
Given
LCM of 4 and 21 = 84
84 x GCF = 84
GCF = 84/84 = 1
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