LCM of 10 and 22 is 110. LCM denotes the smallest positive number which is a multiple of two or more numbers. Students can refer to the article LCM with Examples curated by experts to learn the simple procedure of how to verify the least common multiple of given numbers. Using this article while solving textbook problems enables students to gain in-depth knowledge of the LCM and score good marks in exams. Here, we will learn how to find the least common multiple of 10 and 22 in detail.
What is LCM of 10 and 22?
The answer to this question is 110.
How to Find LCM of 10 and 22?
LCM of 10 and 22 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 10 and 22 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 10 and 22 can be expressed as;
10 = 2 × 5
22 = 2 × 11
LCM (10, 22) = 2 × 5 × 11 = 110
LCM of 10 and 22 Using Division Method
In this method, we divide the numbers 10 and 22 by a common prime number until the remainder is a prime number or one. The product of these divisors represents the least common multiple of 10 and 22.
| 2 | 10 | 22 |
| 5 | 5 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (10, 22) = 2 × 5 × 11 = 110
LCM of 10 and 22 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 10 and 22.
| Multiples of 10 | Multiples of 22 |
| 10 | 22 |
| 20 | 44 |
| 30 | 66 |
| 40 | 88 |
| 50 | 110 |
| 60 | 132 |
| 70 | 154 |
| 80 | 176 |
| 90 | 198 |
| 100 | 220 |
| 110 | 242 |
LCM (10, 22) = 110
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 10 and 22?
Solution: 110 is the smallest number that is divisible by both 10 and 22.
2. The GCD and LCM of the two numbers are 2 and 110. If one number is 10, what is the other number?
Solution: Let the other number be m
We know that
GCD × LCM = 10 × m
m = (GCD × LCM) / 10
m = (2 × 110) / 10
m = 22
Therefore, the other number is 22.
Frequently Asked Questions on LCM of 10 and 22
What is the LCM of 10 and 22?
Is the LCM of 10 and 22 and the HCF of 10 and 22 are same?
How do you find the LCM of 10 and 22 by the prime factorisation method?
In this method, the given natural numbers are expressed as the product of prime factors.
10 = 2 × 5
22 = 2 × 11
LCM (10, 22) = 2 × 5 × 11 = 110
What are the methods used to find the LCM of 10 and 22?
The methods used to find the LCM of 10 and 22 are
Prime Factorisation
Division Method
Listing the Multiples
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