LCM of 20 and 21 is 420. LCM denotes the smallest positive number that is a multiple of two or more numbers. LCM with Examples article is crafted by the subject experts in order to provide trustable study material for the reference of students. Referring to this article on a daily basis helps students master the LCM concept and solve the problems asked in exams with ease. Let us learn how to verify the least common multiple of 20 and 21 in a precise manner here.
What is LCM of 20 and 21?
The Least Common Multiple of 20 and 21 is 420.
How to Find LCM of 20 and 21?
LCM of 20 and 21 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 20 and 21 Using Prime Factorisation Method
In the prime factorisation method, LCM of 20 and 21 can be obtained by multiplying prime factors raised to their respective highest power.
20 = 2 × 2 × 5
21 = 3 × 7
LCM (20, 21) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 20 and 21 Using Division Method
In the division method, to find the LCM, we divide the numbers 20 and 21 by their prime factors until we get the result as one in the complete row. The product of these divisors indicates the least common multiple of 20 and 21.
| 2 | 20 | 21 |
| 2 | 10 | 21 |
| 3 | 5 | 21 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (20, 21) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 20 and 21 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the least common multiple among them. Few multiples of 20 and 21 are given below.
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ………, 380, 400, 420, .…..
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, ………, 378, 399, 420, …….
LCM (20, 21) = 420
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 20 and 21?
Solution: 420 is the smallest number that is divisible by both 20 and 21.
2. The GCD and LCM of the two numbers are 1 and 420. If one number is 20, what is the other number?
Solution: Let the other number be p
We know that,
GCD × LCM = 20 × p
p = (GCD × LCM) / 20
p = (1 × 420) / 20
p = 21
Thus the other number is 21.
Frequently Asked Questions on LCM of 20 and 21
What is the LCM of 20 and 21?
Mention the LCM of 20 and 21 and the HCF of 20 and 21.
What are the methods used to find the least common multiple of 20 and 21?
The methods used to find the least common multiple of 20 and 21 are:
Prime Factorisation
Division method
Listing the Multiples
What is the GCF if the LCM of 20 and 21 is 420?
GCF × LCM = 20 × 21
Given
LCM = 420
GCF × 420 = 20 × 21
GCF = 1
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