LCM of 11 and 17 - Calculation Methods and Solved Examples

Last Updated on Jun 10, 2024
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The LCM of 11 and 17 is 187. The Least Common Multiple, or LCM, is the smallest integer that is a multiple of a given set of numbers. To help students understand this concept better, we've created an article Least Common Multiple (LCM) that breaks down the concept in simple, easy-to-understand terms. In this article, we'll walk through how to find the LCM of 11 and 17 using various methods.

What is the LCM of 11 and 17?

The LCM of 11 and 17 is 187.

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How do you calculate the LCM of 11 and 17?

There are several methods to find the LCM of 11 and 17:

  • Prime Factorisation
  • Division method
  • Listing the Multiples

Prime Factorisation Method to find LCM of 11 and 17

In the prime factorisation method, we express the given numbers as the product of prime factors. So, for the numbers 11 and 17:

11 = 11

17 = 17

LCM (11, 17) = 11 × 17 = 187

Division Method to find LCM of 11 and 17

In the division method, we divide 11 and 17 by a common prime number until we're left with a prime number or one. The product of the divisors gives us the LCM 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

Listing the Multiples to find LCM of 11 and 17

In this method, we list the multiples of each number until we find a common multiple. The multiples of 11 and 17 are:

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

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Example Problems

1. What is the smallest number that is divisible by both 11 and 17?

Answer: The smallest number that is divisible by both 11 and 17 is 187.

2. If the GCD and LCM of two numbers are 1 and 187 respectively, and one of the numbers is 11, what is the other number?

Answer: Let's denote the other number as z.

GCD × LCM = 11 × z

z = (GCD × LCM) / 11

z = (1 × 187) / 11

z = 17

So, the other number is 17.

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Frequently Asked Questions

The LCM of 11 and 17 is 187.

No. The LCM of 11 and 17 is 187 and the HCF of 11 and 17 is 1.

False. The LCM of 11 and 17 is 187.

GCF × LCM = 11 × 17, Given LCM = 187, GCF × 187 = 11 × 17, GCF = 1

The following methods are used to find the LCM of 11 and 17: Prime Factorisation, Division Method, Listing the Multiples

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