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LCM of 13 and 26

LCM of 13 and 26 is the smallest number among all common multiples of 13 and 26. The first few multiples of 13 and 26 are (13, 26, 39, 52, 65, 78, . . . ) and (26, 52, 78, 104, 130, 156, 182, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 26 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 13 and 26
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 13 and 26?

Answer: LCM of 13 and 26 is 26.

Explanation:

The LCM of two non-zero integers, x(13) and y(26), is the smallest positive integer m(26) that is divisible by both x(13) and y(26) without any remainder.

Methods to Find LCM of 13 and 26

The methods to find the LCM of 13 and 26 are explained below.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 13 and 26 by Division Method

To calculate the LCM of 13 and 26 by the division method, we will divide the numbers(13, 26) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 26.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 26. Write this prime number(2) on the left of the given numbers(13 and 26), separated as per the ladder arrangement.
Step 2: If any of the given numbers (13, 26) is a multiple of 2, divide it by 2 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 26 is the product of all prime numbers on the left, i.e. LCM(13, 26) by division method = 2 × 13 = 26.

LCM of 13 and 26 by Listing Multiples

To calculate the LCM of 13 and 26 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, . . . ) and 26 (26, 52, 78, 104, 130, 156, 182, . . . . )
Step 2: The common multiples from the multiples of 13 and 26 are 26, 52, . . .
Step 3: The smallest common multiple of 13 and 26 is 26.

∴ The least common multiple of 13 and 26 = 26.

LCM of 13 and 26 by Prime Factorization

Prime factorization of 13 and 26 is (13) = 13¹ and (2 × 13) = 2¹ × 13¹ respectively. LCM of 13 and 26 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 13¹ = 26.
Hence, the LCM of 13 and 26 by prime factorization is 26.

☛ Also Check:

LCM of 13 and 26 Examples

Example 1: The GCD and LCM of two numbers are 13 and 26 respectively. If one number is 13, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 13 × z
⇒ z = (GCD × LCM)/13
⇒ z = (13 × 26)/13
⇒ z = 26
Therefore, the other number is 26.
Example 2: Verify the relationship between GCF and LCM of 13 and 26.

Solution:

The relation between GCF and LCM of 13 and 26 is given as,
LCM(13, 26) × GCF(13, 26) = Product of 13, 26
Prime factorization of 13 and 26 is given as, 13 = (13) = 13¹ and 26 = (2 × 13) = 2¹ × 13¹
LCM(13, 26) = 26
GCF(13, 26) = 13
LHS = LCM(13, 26) × GCF(13, 26) = 26 × 13 = 338
RHS = Product of 13, 26 = 13 × 26 = 338
⇒ LHS = RHS = 338
Hence, verified.
Example 3: The product of two numbers is 338. If their GCD is 13, what is their LCM?

Solution:

Given: GCD = 13
product of numbers = 338
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 338/13
Therefore, the LCM is 26.
The probable combination for the given case is LCM(13, 26) = 26.

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FAQs on LCM of 13 and 26

What is the LCM of 13 and 26?

The LCM of 13 and 26 is 26. To find the least common multiple of 13 and 26, we need to find the multiples of 13 and 26 (multiples of 13 = 13, 26, 39, 52; multiples of 26 = 26, 52, 78, 104) and choose the smallest multiple that is exactly divisible by 13 and 26, i.e., 26.

What is the Least Perfect Square Divisible by 13 and 26?

The least number divisible by 13 and 26 = LCM(13, 26)
LCM of 13 and 26 = 2 × 13 [Incomplete pair(s): 2, 13]
⇒ Least perfect square divisible by each 13 and 26 = LCM(13, 26) × 2 × 13 = 676 [Square root of 676 = √676 = ±26]
Therefore, 676 is the required number.

If the LCM of 26 and 13 is 26, Find its GCF.

LCM(26, 13) × GCF(26, 13) = 26 × 13
Since the LCM of 26 and 13 = 26
⇒ 26 × GCF(26, 13) = 338
Therefore, the greatest common factor (GCF) = 338/26 = 13.

What is the Relation Between GCF and LCM of 13, 26?

The following equation can be used to express the relation between GCF and LCM of 13 and 26, i.e. GCF × LCM = 13 × 26.

How to Find the LCM of 13 and 26 by Prime Factorization?

To find the LCM of 13 and 26 using prime factorization, we will find the prime factors, (13 = 13) and (26 = 2 × 13). LCM of 13 and 26 is the product of prime factors raised to their respective highest exponent among the numbers 13 and 26.
⇒ LCM of 13, 26 = 2¹ × 13¹ = 26.

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