LCM of 2 and 13

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.

lcm of 2 and 13

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

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

Q1

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

Q2

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

Q3

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

Q4

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.

Q5

What are the methods used to find the LCM of 2 and 13?

The methods used to find the LCM of 2 and 13 are prime factorisation, division and listing the multiples.

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