LCM of 2 and 13 is 26. The LCM value is the number divisible evenly by the two given numbers. By writing down the multiples of the numbers, the least common multiples of 2 and 13 can be figured out. (2, 4, 6, 8, 10, 12, 14, ….) and (13, 26, 39, 52, 65, 78, 91,….) are the multiples of 2 and 13. The LCM of two numbers based on the prime factorization, division and by listing the multiples are provided here for a good understanding among students.
Also read: Least common multiple
What is LCM of 2 and 13?
The answer to this question is 26. The LCM of 2 and 13 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 2 and 13, is the smallest positive integer 26 which is divisible by both 2 and 13 with no remainder.
How to Find LCM of 2 and 13?
LCM of 2 and 13 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 2 and 13 Using Prime Factorisation Method
The prime factorisation of 2 and 13, respectively, is given by:
2 = 2¹
13 = 13¹
LCM (2, 13) = 26
LCM of 2 and 13 Using Division Method
We’ll divide the numbers (2, 13) by their prime factors to get the LCM of 2 and 13 using the division method (preferably common). The LCM of 2 and 13 is calculated by multiplying these divisors.
|
2 |
2 |
13 |
|
13 |
1 |
13 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (2, 13) = 26
LCM of 2 and 13 Using Listing the Multiples
To calculate the LCM of 2 and 13 by listing out the common multiples, list the multiples as shown below.
Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, …..
Multiples of 13 = 13, 26, 39, 52, 65, …….
LCM (2, 13) = 26
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 2 and 13 Solved Examples
Question: If LCM = 26, GCD = 1 and one number is 2, find the other.
Solution:
Given
LCM = 26
GCD = 1
Consider y as the other number
LCM x GCD = 2 x y
y = (LCM x GCD)/2
y = (26 x 1)/2
y = 13
Hence, the other number is 13.
Frequently Asked Questions on LCM of 2 and 13
What is the LCM of 2 and 13 using the prime factorization method?
To find the LCM using the prime factorization, we should know the prime factors.
2 = 2¹
13 = 13¹
LCM of 2 and 13 is the product of prime factors raised to the highest exponent among the numbers 2 and 13
LCM of 2 and 13 = 26
If the LCM of 2 and 13 is 26, find the GCF.
LCM x GCF = 2 x 13
Given
LCM of 2 and 13 = 26
26 x GCF = 26
GCF = 26/26 = 1
Show the relation between GCF and LCM of 2 and 13.
The relation between GCF and LCM of 2 and 13 is
LCM x GCF = 2 x 13
LCM x GCF = 26
If GCD = 1 and product of two numbers = 26, find the LCM.
Given
GCD = 1
Product = 26
GCD x LCM = Product
LCM = Product/GCD
LCM = 26/1 = 26
Hence, the LCM is 26.
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