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LCM of 26 and 169

LCM of 26 and 169 is the smallest number among all common multiples of 26 and 169. The first few multiples of 26 and 169 are (26, 52, 78, 104, . . . ) and (169, 338, 507, 676, 845, . . . ) respectively. There are 3 commonly used methods to find LCM of 26 and 169 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 26 and 169
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 26 and 169?

Answer: LCM of 26 and 169 is 338.

Explanation:

The LCM of two non-zero integers, x(26) and y(169), is the smallest positive integer m(338) that is divisible by both x(26) and y(169) without any remainder.

Methods to Find LCM of 26 and 169

The methods to find the LCM of 26 and 169 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 26 and 169 by Listing Multiples

To calculate the LCM of 26 and 169 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 169 (169, 338, 507, 676, 845, . . . . )
Step 2: The common multiples from the multiples of 26 and 169 are 338, 676, . . .
Step 3: The smallest common multiple of 26 and 169 is 338.

∴ The least common multiple of 26 and 169 = 338.

LCM of 26 and 169 by Division Method

To calculate the LCM of 26 and 169 by the division method, we will divide the numbers(26, 169) by their prime factors (preferably common). The product of these divisors gives the LCM of 26 and 169.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 26 and 169. Write this prime number(2) on the left of the given numbers(26 and 169), separated as per the ladder arrangement.
Step 2: If any of the given numbers (26, 169) 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 169 is the product of all prime numbers on the left, i.e. LCM(26, 169) by division method = 2 × 13 × 13 = 338.

LCM of 26 and 169 by Prime Factorization

Prime factorization of 26 and 169 is (2 × 13) = 2¹ × 13¹ and (13 × 13) = 13² respectively. LCM of 26 and 169 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 13² = 338.
Hence, the LCM of 26 and 169 by prime factorization is 338.

☛ Also Check:

LCM of 26 and 169 Examples

Example 1: The product of two numbers is 4394. If their GCD is 13, what is their LCM?

Solution:

Given: GCD = 13
product of numbers = 4394
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 4394/13
Therefore, the LCM is 338.
The probable combination for the given case is LCM(26, 169) = 338.
Example 2: Verify the relationship between GCF and LCM of 26 and 169.

Solution:

The relation between GCF and LCM of 26 and 169 is given as,
LCM(26, 169) × GCF(26, 169) = Product of 26, 169
Prime factorization of 26 and 169 is given as, 26 = (2 × 13) = 2¹ × 13¹ and 169 = (13 × 13) = 13²
LCM(26, 169) = 338
GCF(26, 169) = 13
LHS = LCM(26, 169) × GCF(26, 169) = 338 × 13 = 4394
RHS = Product of 26, 169 = 26 × 169 = 4394
⇒ LHS = RHS = 4394
Hence, verified.
Example 3: The GCD and LCM of two numbers are 13 and 338 respectively. If one number is 26, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 26 × a
⇒ a = (GCD × LCM)/26
⇒ a = (13 × 338)/26
⇒ a = 169
Therefore, the other number is 169.

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FAQs on LCM of 26 and 169

What is the LCM of 26 and 169?

The LCM of 26 and 169 is 338. To find the LCM (least common multiple) of 26 and 169, we need to find the multiples of 26 and 169 (multiples of 26 = 26, 52, 78, 104 . . . . 338; multiples of 169 = 169, 338, 507, 676) and choose the smallest multiple that is exactly divisible by 26 and 169, i.e., 338.

How to Find the LCM of 26 and 169 by Prime Factorization?

To find the LCM of 26 and 169 using prime factorization, we will find the prime factors, (26 = 2 × 13) and (169 = 13 × 13). LCM of 26 and 169 is the product of prime factors raised to their respective highest exponent among the numbers 26 and 169.
⇒ LCM of 26, 169 = 2¹ × 13² = 338.

What is the Least Perfect Square Divisible by 26 and 169?

The least number divisible by 26 and 169 = LCM(26, 169)
LCM of 26 and 169 = 2 × 13 × 13 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 26 and 169 = LCM(26, 169) × 2 = 676 [Square root of 676 = √676 = ±26]
Therefore, 676 is the required number.

What is the Relation Between GCF and LCM of 26, 169?

The following equation can be used to express the relation between GCF and LCM of 26 and 169, i.e. GCF × LCM = 26 × 169.

If the LCM of 169 and 26 is 338, Find its GCF.

LCM(169, 26) × GCF(169, 26) = 169 × 26
Since the LCM of 169 and 26 = 338
⇒ 338 × GCF(169, 26) = 4394
Therefore, the greatest common factor (GCF) = 4394/338 = 13.

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