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LCM of 11 and 17

LCM of 11 and 17 is the smallest number among all common multiples of 11 and 17. The first few multiples of 11 and 17 are (11, 22, 33, 44, 55, 66, 77, . . . ) and (17, 34, 51, 68, 85, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 17 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 11 and 17
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 11 and 17?

Answer: LCM of 11 and 17 is 187.

Explanation:

The LCM of two non-zero integers, x(11) and y(17), is the smallest positive integer m(187) that is divisible by both x(11) and y(17) without any remainder.

Methods to Find LCM of 11 and 17

Let's look at the different methods for finding the LCM of 11 and 17.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 11 and 17 by Division Method

To calculate the LCM of 11 and 17 by the division method, we will divide the numbers(11, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 17.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 17. Write this prime number(11) on the left of the given numbers(11 and 17), separated as per the ladder arrangement.
Step 2: If any of the given numbers (11, 17) is a multiple of 11, divide it by 11 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 11 and 17 is the product of all prime numbers on the left, i.e. LCM(11, 17) by division method = 11 × 17 = 187.

LCM of 11 and 17 by Prime Factorization

Prime factorization of 11 and 17 is (11) = 11¹ and (17) = 17¹ respectively. LCM of 11 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 11¹ × 17¹ = 187.
Hence, the LCM of 11 and 17 by prime factorization is 187.

LCM of 11 and 17 by Listing Multiples

To calculate the LCM of 11 and 17 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 11 (11, 22, 33, 44, 55, 66, 77, . . . ) and 17 (17, 34, 51, 68, 85, . . . . )
Step 2: The common multiples from the multiples of 11 and 17 are 187, 374, . . .
Step 3: The smallest common multiple of 11 and 17 is 187.

∴ The least common multiple of 11 and 17 = 187.

☛ Also Check:

LCM of 11 and 17 Examples

Example 1: The GCD and LCM of two numbers are 1 and 187 respectively. If one number is 11, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 11 × a
⇒ a = (GCD × LCM)/11
⇒ a = (1 × 187)/11
⇒ a = 17
Therefore, the other number is 17.
Example 2: The product of two numbers is 187. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 187
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 187/1
Therefore, the LCM is 187.
The probable combination for the given case is LCM(11, 17) = 187.
Example 3: Verify the relationship between GCF and LCM of 11 and 17.

Solution:

The relation between GCF and LCM of 11 and 17 is given as,
LCM(11, 17) × GCF(11, 17) = Product of 11, 17
Prime factorization of 11 and 17 is given as, 11 = (11) = 11¹ and 17 = (17) = 17¹
LCM(11, 17) = 187
GCF(11, 17) = 1
LHS = LCM(11, 17) × GCF(11, 17) = 187 × 1 = 187
RHS = Product of 11, 17 = 11 × 17 = 187
⇒ LHS = RHS = 187
Hence, verified.

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FAQs on LCM of 11 and 17

What is the LCM of 11 and 17?

The LCM of 11 and 17 is 187. To find the least common multiple (LCM) of 11 and 17, we need to find the multiples of 11 and 17 (multiples of 11 = 11, 22, 33, 44 . . . . 187; multiples of 17 = 17, 34, 51, 68 . . . . 187) and choose the smallest multiple that is exactly divisible by 11 and 17, i.e., 187.

Which of the following is the LCM of 11 and 17? 24, 40, 187, 30

The value of LCM of 11, 17 is the smallest common multiple of 11 and 17. The number satisfying the given condition is 187.

If the LCM of 17 and 11 is 187, Find its GCF.

LCM(17, 11) × GCF(17, 11) = 17 × 11
Since the LCM of 17 and 11 = 187
⇒ 187 × GCF(17, 11) = 187
Therefore, the GCF = 187/187 = 1.

What are the Methods to Find LCM of 11 and 17?

The commonly used methods to find the LCM of 11 and 17 are:

Listing Multiples
Prime Factorization Method
Division Method

What is the Relation Between GCF and LCM of 11, 17?

The following equation can be used to express the relation between GCF and LCM of 11 and 17, i.e. GCF × LCM = 11 × 17.

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