LCM of 11 and 23 is 253. LCM denotes the smallest positive number which is a multiple of two or more numbers. The article Least Common Multiple (LCM) aims to provide a clear cut idea of the LCM concept, which is essential to score high marks in the exams. The top-grade faculty with good knowledge of the LCM concept designed this article as per the students understanding abilities. In this article, let us learn how to calculate the least common multiple of 11 and 23 with a complete explanation.
What is LCM of 11 and 23?
The answer to this question is 253.
How to Find LCM of 11 and 23?
LCM of 11 and 23 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 11 and 23 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence, the numbers 11 and 23 can be expressed as;
11 = 11
23 = 23
LCM (11, 23) = 11 × 23 = 253
LCM of 11 and 23 Using Division Method
In this method, we divide the numbers 11 and 23 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 11 and 23.
| 11 | 11 | 23 |
| 23 | 1 | 23 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (11, 23) = 11 × 23 = 253
LCM of 11 and 23 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 11 and 23.
Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, ………, 231, 242, 253, ………….
Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230, 253, ………..
LCM (11, 23) = 253
Related Articles
Prime Factorization 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 11 and 23?
Solution: 253 is the smallest number that is divisible by both 11 and 23.
2. The GCD and LCM of the two numbers are 1 and 253. If one number is 23, what is the other number?
Solution: Let the other number be k
We know that,
GCD × LCM = 23 × k
k = (GCD × LCM) / 23
k = ( 1 × 253) / 23
k = 11
Hence the other number is 11.
Frequently Asked Questions on LCM of 11 and 23
What is the LCM of 11 and 23?
Is the LCM of 11 and 23 the same as the HCF of 11 and 23?
How to find the LCM of 11 and 23 by prime factorisation?
In the prime factorisation method, the given numbers are expressed as the product of prime factors
11 = 11
23 = 23
LCM (11, 23) = 11 × 23 = 253
Hence, 253 is the LCM of 11 and 23 by prime factorisation
Name the methods to find the LCM of 11 and 23.
The methods used to find the LCM of 11 and 23 are
Prime Factorisation
Division Method
Listing the Multiples
Calculate the GCF if the LCM of 11 and 23 is 253.
GCF × LCM = 11 × 23
Given
LCM = 253
GCF × 253 = 11 × 23
GCF = 1
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