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LCM of 49 and 13

LCM of 49 and 13 is the smallest number among all common multiples of 49 and 13. The first few multiples of 49 and 13 are (49, 98, 147, 196, 245, . . . ) and (13, 26, 39, 52, 65, 78, 91, . . . ) respectively. There are 3 commonly used methods to find LCM of 49 and 13 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 49 and 13
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 49 and 13?

Answer: LCM of 49 and 13 is 637.

Explanation:

The LCM of two non-zero integers, x(49) and y(13), is the smallest positive integer m(637) that is divisible by both x(49) and y(13) without any remainder.

Methods to Find LCM of 49 and 13

Let's look at the different methods for finding the LCM of 49 and 13.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 49 and 13 by Listing Multiples

To calculate the LCM of 49 and 13 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 49 (49, 98, 147, 196, 245, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )
Step 2: The common multiples from the multiples of 49 and 13 are 637, 1274, . . .
Step 3: The smallest common multiple of 49 and 13 is 637.

∴ The least common multiple of 49 and 13 = 637.

LCM of 49 and 13 by Prime Factorization

Prime factorization of 49 and 13 is (7 × 7) = 7² and (13) = 13¹ respectively. LCM of 49 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 7² × 13¹ = 637.
Hence, the LCM of 49 and 13 by prime factorization is 637.

LCM of 49 and 13 by Division Method

To calculate the LCM of 49 and 13 by the division method, we will divide the numbers(49, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 49 and 13.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 49 and 13. Write this prime number(7) on the left of the given numbers(49 and 13), separated as per the ladder arrangement.
Step 2: If any of the given numbers (49, 13) is a multiple of 7, divide it by 7 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 49 and 13 is the product of all prime numbers on the left, i.e. LCM(49, 13) by division method = 7 × 7 × 13 = 637.

☛ Also Check:

LCM of 49 and 13 Examples

Example 1: Verify the relationship between GCF and LCM of 49 and 13.

Solution:

The relation between GCF and LCM of 49 and 13 is given as,
LCM(49, 13) × GCF(49, 13) = Product of 49, 13
Prime factorization of 49 and 13 is given as, 49 = (7 × 7) = 7² and 13 = (13) = 13¹
LCM(49, 13) = 637
GCF(49, 13) = 1
LHS = LCM(49, 13) × GCF(49, 13) = 637 × 1 = 637
RHS = Product of 49, 13 = 49 × 13 = 637
⇒ LHS = RHS = 637
Hence, verified.
Example 2: The product of two numbers is 637. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 637
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 637/1
Therefore, the LCM is 637.
The probable combination for the given case is LCM(49, 13) = 637.
Example 3: The GCD and LCM of two numbers are 1 and 637 respectively. If one number is 49, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 49 × y
⇒ y = (GCD × LCM)/49
⇒ y = (1 × 637)/49
⇒ y = 13
Therefore, the other number is 13.

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FAQs on LCM of 49 and 13

What is the LCM of 49 and 13?

The LCM of 49 and 13 is 637. To find the LCM (least common multiple) of 49 and 13, we need to find the multiples of 49 and 13 (multiples of 49 = 49, 98, 147, 196 . . . . 637; multiples of 13 = 13, 26, 39, 52 . . . . 637) and choose the smallest multiple that is exactly divisible by 49 and 13, i.e., 637.

Which of the following is the LCM of 49 and 13? 16, 45, 637, 3

The value of LCM of 49, 13 is the smallest common multiple of 49 and 13. The number satisfying the given condition is 637.

What are the Methods to Find LCM of 49 and 13?

The commonly used methods to find the LCM of 49 and 13 are:

Prime Factorization Method
Listing Multiples
Division Method

If the LCM of 13 and 49 is 637, Find its GCF.

LCM(13, 49) × GCF(13, 49) = 13 × 49
Since the LCM of 13 and 49 = 637
⇒ 637 × GCF(13, 49) = 637
Therefore, the GCF = 637/637 = 1.

What is the Least Perfect Square Divisible by 49 and 13?

The least number divisible by 49 and 13 = LCM(49, 13)
LCM of 49 and 13 = 7 × 7 × 13 [Incomplete pair(s): 13]
⇒ Least perfect square divisible by each 49 and 13 = LCM(49, 13) × 13 = 8281 [Square root of 8281 = √8281 = ±91]
Therefore, 8281 is the required number.

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