LCM of 20 and 22 is 220. LCM denotes the smallest positive number that is a multiple of two or more numbers. Practising the problems using LCM with Examples is the ultimate need for students who aspire to enhance skills which are crucial from an exam point of view. This article explains the LCM concept with suitable examples in accordance with the students’ understanding capacity. Let us grasp the method of determining the least common multiple of 20 and 22 in a precise manner here.
What is LCM of 20 and 22?
The Least Common Multiple of 20 and 22 is 220.
How to Find LCM of 20 and 22?
LCM of 20 and 22 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 20 and 22 Using Prime Factorisation Method
In the prime factorisation method, LCM of 20 and 22 can be obtained by multiplying prime factors raised to their respective highest power.
20 = 2 × 2 × 5
22 = 2 × 11
LCM (20, 22) = 2 × 2 × 5 × 11 = 220
LCM of 20 and 22 Using Division Method
In the division method, to find the LCM, we divide the numbers 20 and 22 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 22.
| 2 | 20 | 22 |
| 2 | 10 | 11 |
| 5 | 5 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (20, 22) = 2 × 2 × 5 × 11 = 220
LCM of 20 and 22 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the least common multiple among them. Let us have a look at the multiples of 20 and 22 given below.
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, …………
Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220, …………..
LCM (20, 22) = 220
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 22?
Solution: 220 is the smallest number that is divisible by both 20 and 22.
2. The GCD and LCM of the two numbers are 2 and 220. 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 = (2 × 220) / 20
p = 22
Thus the other number is 22.
Frequently Asked Questions on LCM of 20 and 22
What is the LCM of 20 and 22?
Is the LCM of 20 and 22 the same as the HCF of 20 and 22?
What are the methods used to find the least common multiple of 20 and 22?
The methods used to find the least common multiple of 20 and 22 are:
Prime Factorisation
Division method
Listing the Multiples
Calculate the GCF if the LCM of 20 and 22 is 220.
GCF × LCM = 20 × 22
Given
LCM = 220
GCF × 220 = 20 × 22
GCF = 2
Find the LCM of 20 and 22 using the prime factorisation method.
In this method, we express the numbers as the product of prime factors to find the LCM
20 = 2 × 2 × 5
22 = 2 × 11
LCM (20, 22) = 2 × 2 × 5 × 11 = 220
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