LCM of 26 and 169 is 338. To learn how to determine the least common multiple and highest common factors of given numbers using prime factorisation, division method and listing multiples, students are recommended to follow the article HCF and LCM prepared by expert faculty. Referring to this article, students can grasp in-depth knowledge based on LCM and HCF. Let us have a glance at how to find the least common multiple of 26 and 169 using a simple procedure in this article.
What is LCM of 26 and 169?
The Least Common Multiple of 26 and 169 is 338.
How to Find LCM of 26 and 169?
We can determine the LCM of 26 and 169 by using the methods given below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 26 and 169 Using Prime Factorisation Method
In the prime factorisation method, LCM of 26 and 169 can be obtained by multiplying prime factors raised to their respective highest power.
26 = 2 × 13
169 = 13 × 13
LCM (26, 169) = 2 × 13 × 13 = 338
LCM of 26 and 169 Using Division Method
In the division method, to calculate the LCM of 26 and 169, we divide the numbers 26 and 169 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 26 and 169.
|
2 |
26 |
169 |
|
13 |
13 |
169 |
|
13 |
1 |
13 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (26,169) = 2 × 13 × 13 = 338
LCM of 26 and 169 Using Listing the Multiples
Here, we list down the multiples of given numbers to find the least common multiple among them. Let us glance at the multiples of 26 and 169 given below.
Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260, 286, 312, 338, ………
Multiples of 169: 169, 338, 507, 676, 845,……..
LCM (26, 169) = 338
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: The GCD and LCM of two numbers are 13 and 338. If one number is 26, calculate the other number.
Solution: Let the other number be p
We know that,
GCD × LCM = 26 × p
p = (GCD × LCM) / 26
p = (13 × 338) / 26
p = 169
Hence the other number is 169.
Q. 2: Find the LCM of 26 and 169 using prime factorisation method.
Solution: The LCM of 26 and 169 using prime factorisation method can be determined as below
26 = 2 × 13
169 = 13 × 13
LCM (26, 169) = 2 × 13 × 13 = 338
Therefore the least common multiple of 26 and 169 by prime factorisation is 338.
Frequently Asked Questions on LCM of 26 and 169
What is the LCM of 26 and 169?
What are the methods used to find the LCM of 26 and 169?
The following methods are used to find the LCM of 26 and 169
Prime Factorisation
Division Method
Listing the multiples
Is 338 the LCM of 26 and 169?
Find the GCF if the LCM of 26 and 169 is 338.
LCM × GCF = 26 × 169
Given
LCM of 26 and 169 = 338
338 × GCF = 26 × 169
GCF = 13
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