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LCM of 13 and 19

LCM of 13 and 19 is the smallest number among all common multiples of 13 and 19. The first few multiples of 13 and 19 are (13, 26, 39, 52, 65, 78, 91, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 19 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 13 and 19
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 13 and 19?

Answer: LCM of 13 and 19 is 247.

Explanation:

The LCM of two non-zero integers, x(13) and y(19), is the smallest positive integer m(247) that is divisible by both x(13) and y(19) without any remainder.

Methods to Find LCM of 13 and 19

The methods to find the LCM of 13 and 19 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 13 and 19 by Listing Multiples

To calculate the LCM of 13 and 19 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, 65, 78, 91, . . . ) and 19 (19, 38, 57, 76, 95, . . . . )
Step 2: The common multiples from the multiples of 13 and 19 are 247, 494, . . .
Step 3: The smallest common multiple of 13 and 19 is 247.

∴ The least common multiple of 13 and 19 = 247.

LCM of 13 and 19 by Division Method

To calculate the LCM of 13 and 19 by the division method, we will divide the numbers(13, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 19.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 19. Write this prime number(13) on the left of the given numbers(13 and 19), separated as per the ladder arrangement.
Step 2: If any of the given numbers (13, 19) 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 19 is the product of all prime numbers on the left, i.e. LCM(13, 19) by division method = 13 × 19 = 247.

LCM of 13 and 19 by Prime Factorization

Prime factorization of 13 and 19 is (13) = 13¹ and (19) = 19¹ respectively. LCM of 13 and 19 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 13¹ × 19¹ = 247.
Hence, the LCM of 13 and 19 by prime factorization is 247.

☛ Also Check:

LCM of 13 and 19 Examples

Example 1: Verify the relationship between GCF and LCM of 13 and 19.

Solution:

The relation between GCF and LCM of 13 and 19 is given as,
LCM(13, 19) × GCF(13, 19) = Product of 13, 19
Prime factorization of 13 and 19 is given as, 13 = (13) = 13¹ and 19 = (19) = 19¹
LCM(13, 19) = 247
GCF(13, 19) = 1
LHS = LCM(13, 19) × GCF(13, 19) = 247 × 1 = 247
RHS = Product of 13, 19 = 13 × 19 = 247
⇒ LHS = RHS = 247
Hence, verified.
Example 2: The product of two numbers is 247. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 247
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 247/1
Therefore, the LCM is 247.
The probable combination for the given case is LCM(13, 19) = 247.
Example 3: The GCD and LCM of two numbers are 1 and 247 respectively. If one number is 13, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 13 × a
⇒ a = (GCD × LCM)/13
⇒ a = (1 × 247)/13
⇒ a = 19
Therefore, the other number is 19.

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FAQs on LCM of 13 and 19

What is the LCM of 13 and 19?

The LCM of 13 and 19 is 247. To find the LCM (least common multiple) of 13 and 19, we need to find the multiples of 13 and 19 (multiples of 13 = 13, 26, 39, 52 . . . . 247; multiples of 19 = 19, 38, 57, 76 . . . . 247) and choose the smallest multiple that is exactly divisible by 13 and 19, i.e., 247.

What are the Methods to Find LCM of 13 and 19?

The commonly used methods to find the LCM of 13 and 19 are:

Prime Factorization Method
Division Method
Listing Multiples

Which of the following is the LCM of 13 and 19? 50, 247, 40, 12

The value of LCM of 13, 19 is the smallest common multiple of 13 and 19. The number satisfying the given condition is 247.

If the LCM of 19 and 13 is 247, Find its GCF.

LCM(19, 13) × GCF(19, 13) = 19 × 13
Since the LCM of 19 and 13 = 247
⇒ 247 × GCF(19, 13) = 247
Therefore, the GCF (greatest common factor) = 247/247 = 1.

What is the Relation Between GCF and LCM of 13, 19?

The following equation can be used to express the relation between GCF and LCM of 13 and 19, i.e. GCF × LCM = 13 × 19.

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