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LCM of 13 and 17

LCM of 13 and 17 is the smallest number among all common multiples of 13 and 17. The first few multiples of 13 and 17 are (13, 26, 39, 52, . . . ) and (17, 34, 51, 68, 85, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 17 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 13 and 17
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 13 and 17?

Answer: LCM of 13 and 17 is 221.

Explanation:

The LCM of two non-zero integers, x(13) and y(17), is the smallest positive integer m(221) that is divisible by both x(13) and y(17) without any remainder.

Methods to Find LCM of 13 and 17

The methods to find the LCM of 13 and 17 are explained below.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 13 and 17 by Listing Multiples

To calculate the LCM of 13 and 17 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 13 (13, 26, 39, 52, . . . ) and 17 (17, 34, 51, 68, 85, . . . . )
Step 2: The common multiples from the multiples of 13 and 17 are 221, 442, . . .
Step 3: The smallest common multiple of 13 and 17 is 221.

∴ The least common multiple of 13 and 17 = 221.

LCM of 13 and 17 by Prime Factorization

Prime factorization of 13 and 17 is (13) = 13¹ and (17) = 17¹ respectively. LCM of 13 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 13¹ × 17¹ = 221.
Hence, the LCM of 13 and 17 by prime factorization is 221.

LCM of 13 and 17 by Division Method

To calculate the LCM of 13 and 17 by the division method, we will divide the numbers(13, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 17.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 17. Write this prime number(13) on the left of the given numbers(13 and 17), separated as per the ladder arrangement.
Step 2: If any of the given numbers (13, 17) is a multiple of 13, divide it by 13 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 13 and 17 is the product of all prime numbers on the left, i.e. LCM(13, 17) by division method = 13 × 17 = 221.

☛ Also Check:

LCM of 13 and 17 Examples

Example 1: Verify the relationship between GCF and LCM of 13 and 17.

Solution:

The relation between GCF and LCM of 13 and 17 is given as,
LCM(13, 17) × GCF(13, 17) = Product of 13, 17
Prime factorization of 13 and 17 is given as, 13 = (13) = 13¹ and 17 = (17) = 17¹
LCM(13, 17) = 221
GCF(13, 17) = 1
LHS = LCM(13, 17) × GCF(13, 17) = 221 × 1 = 221
RHS = Product of 13, 17 = 13 × 17 = 221
⇒ LHS = RHS = 221
Hence, verified.
Example 2: The product of two numbers is 221. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 221
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 221/1
Therefore, the LCM is 221.
The probable combination for the given case is LCM(13, 17) = 221.
Example 3: The GCD and LCM of two numbers are 1 and 221 respectively. If one number is 17, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 17 × z
⇒ z = (GCD × LCM)/17
⇒ z = (1 × 221)/17
⇒ z = 13
Therefore, the other number is 13.

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FAQs on LCM of 13 and 17

What is the LCM of 13 and 17?

The LCM of 13 and 17 is 221. To find the least common multiple of 13 and 17, we need to find the multiples of 13 and 17 (multiples of 13 = 13, 26, 39, 52 . . . . 221; multiples of 17 = 17, 34, 51, 68 . . . . 221) and choose the smallest multiple that is exactly divisible by 13 and 17, i.e., 221.

What are the Methods to Find LCM of 13 and 17?

The commonly used methods to find the LCM of 13 and 17 are:

Listing Multiples
Prime Factorization Method
Division Method

If the LCM of 17 and 13 is 221, Find its GCF.

LCM(17, 13) × GCF(17, 13) = 17 × 13
Since the LCM of 17 and 13 = 221
⇒ 221 × GCF(17, 13) = 221
Therefore, the greatest common factor = 221/221 = 1.

Which of the following is the LCM of 13 and 17? 221, 5, 12, 2

The value of LCM of 13, 17 is the smallest common multiple of 13 and 17. The number satisfying the given condition is 221.

How to Find the LCM of 13 and 17 by Prime Factorization?

To find the LCM of 13 and 17 using prime factorization, we will find the prime factors, (13 = 13) and (17 = 17). LCM of 13 and 17 is the product of prime factors raised to their respective highest exponent among the numbers 13 and 17.
⇒ LCM of 13, 17 = 13¹ × 17¹ = 221.

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