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LCM of 26 and 39

LCM of 26 and 39 is the smallest number among all common multiples of 26 and 39. The first few multiples of 26 and 39 are (26, 52, 78, 104, . . . ) and (39, 78, 117, 156, 195, . . . ) respectively. There are 3 commonly used methods to find LCM of 26 and 39 - by prime factorization, by division method, and by listing multiples.

1.	LCM of 26 and 39
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 26 and 39?

Answer: LCM of 26 and 39 is 78.

Explanation:

The LCM of two non-zero integers, x(26) and y(39), is the smallest positive integer m(78) that is divisible by both x(26) and y(39) without any remainder.

Methods to Find LCM of 26 and 39

The methods to find the LCM of 26 and 39 are explained below.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 26 and 39 by Prime Factorization

Prime factorization of 26 and 39 is (2 × 13) = 2¹ × 13¹ and (3 × 13) = 3¹ × 13¹ respectively. LCM of 26 and 39 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 13¹ = 78.
Hence, the LCM of 26 and 39 by prime factorization is 78.

LCM of 26 and 39 by Division Method

To calculate the LCM of 26 and 39 by the division method, we will divide the numbers(26, 39) by their prime factors (preferably common). The product of these divisors gives the LCM of 26 and 39.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 26 and 39. Write this prime number(2) on the left of the given numbers(26 and 39), separated as per the ladder arrangement.
Step 2: If any of the given numbers (26, 39) 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 26 and 39 is the product of all prime numbers on the left, i.e. LCM(26, 39) by division method = 2 × 3 × 13 = 78.

LCM of 26 and 39 by Listing Multiples

To calculate the LCM of 26 and 39 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 26 (26, 52, 78, 104, . . . ) and 39 (39, 78, 117, 156, 195, . . . . )
Step 2: The common multiples from the multiples of 26 and 39 are 78, 156, . . .
Step 3: The smallest common multiple of 26 and 39 is 78.

∴ The least common multiple of 26 and 39 = 78.

☛ Also Check:

LCM of 26 and 39 Examples

Example 1: Verify the relationship between GCF and LCM of 26 and 39.

Solution:

The relation between GCF and LCM of 26 and 39 is given as,
LCM(26, 39) × GCF(26, 39) = Product of 26, 39
Prime factorization of 26 and 39 is given as, 26 = (2 × 13) = 2¹ × 13¹ and 39 = (3 × 13) = 3¹ × 13¹
LCM(26, 39) = 78
GCF(26, 39) = 13
LHS = LCM(26, 39) × GCF(26, 39) = 78 × 13 = 1014
RHS = Product of 26, 39 = 26 × 39 = 1014
⇒ LHS = RHS = 1014
Hence, verified.
Example 2: The product of two numbers is 1014. If their GCD is 13, what is their LCM?

Solution:

Given: GCD = 13
product of numbers = 1014
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1014/13
Therefore, the LCM is 78.
The probable combination for the given case is LCM(26, 39) = 78.
Example 3: The GCD and LCM of two numbers are 13 and 78 respectively. If one number is 26, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 26 × y
⇒ y = (GCD × LCM)/26
⇒ y = (13 × 78)/26
⇒ y = 39
Therefore, the other number is 39.

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FAQs on LCM of 26 and 39

What is the LCM of 26 and 39?

The LCM of 26 and 39 is 78. To find the least common multiple of 26 and 39, we need to find the multiples of 26 and 39 (multiples of 26 = 26, 52, 78, 104; multiples of 39 = 39, 78, 117, 156) and choose the smallest multiple that is exactly divisible by 26 and 39, i.e., 78.

How to Find the LCM of 26 and 39 by Prime Factorization?

To find the LCM of 26 and 39 using prime factorization, we will find the prime factors, (26 = 2 × 13) and (39 = 3 × 13). LCM of 26 and 39 is the product of prime factors raised to their respective highest exponent among the numbers 26 and 39.
⇒ LCM of 26, 39 = 2¹ × 3¹ × 13¹ = 78.

Which of the following is the LCM of 26 and 39? 28, 5, 3, 78

The value of LCM of 26, 39 is the smallest common multiple of 26 and 39. The number satisfying the given condition is 78.

What is the Least Perfect Square Divisible by 26 and 39?

The least number divisible by 26 and 39 = LCM(26, 39)
LCM of 26 and 39 = 2 × 3 × 13 [Incomplete pair(s): 2, 3, 13]
⇒ Least perfect square divisible by each 26 and 39 = LCM(26, 39) × 2 × 3 × 13 = 6084 [Square root of 6084 = √6084 = ±78]
Therefore, 6084 is the required number.

If the LCM of 39 and 26 is 78, Find its GCF.

LCM(39, 26) × GCF(39, 26) = 39 × 26
Since the LCM of 39 and 26 = 78
⇒ 78 × GCF(39, 26) = 1014
Therefore, the GCF = 1014/78 = 13.

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