LCM of 11 and 17 is 187. The least common multiple denotes the smallest positive integer, which is multiple in a given set of numbers. The article Least Common Multiple (LCM) is tailored by experts in simple language to make it easy for the students. This article provides a clear explanation of the LCM concept that will help students understand it in a better way. Here we will learn how to determine the least common multiple of 11 and 17 using solved examples and FAQs.
What is LCM of 11 and 17?
The Least Common Multiple of 11 and 17 is 187.
How to Find LCM of 11 and 17?
The LCM of 11 and 17 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 11 and 17 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Therefore, the numbers 11 and 17 can be expressed as;
11 = 11
17 = 17
LCM (11, 17) = 11 × 17 = 187
LCM of 11 and 17 Using Division Method
In the division method, we divide the numbers 11 and 17 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 11 and 17.
| 11 | 11 | 17 |
| 17 | 1 | 17 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (11, 17) = 11 × 17 = 187
LCM of 11 and 17 Using Listing the Multiples
In this method, we list down the multiples of each number until the first common multiple is found among them. The multiples of 11 and 17 are as follows:
Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, ………,165, 176, 187, …..
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187,………
LCM (11, 17) = 187
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 11 and 17?
Solution: 187 is the smallest number that is divisible by both 11 and 17.
2. The GCD and LCM of the two numbers are 1 and 187. If one number is 11, calculate the other number.
Solution: Let the other number be z
We know that,
GCD × LCM = 11 × z
z = (GCD × LCM) / 11
z = (1 × 187) / 11
z = 17
Hence, the other number is 17.
Frequently Asked Questions on LCM of 11 and 17
What is the LCM of 11 and 17?
Is the LCM of 11 and 17 same as the HCF of 11 and 17?
197 is the LCM of 11 and 17. True or False.
What is the GCF if the LCM of 11 and 17 is 187?
GCF × LCM = 11 × 17
Given
LCM = 187
GCF × 187 = 11 × 17
GCF = 1
Name the methods used to find the LCM of 11 and 17.
The following methods are used to find the LCM of 11 and 17
Prime Factorisation
Division Method
Listing the Multiples
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