LCM of 8 and 13 is 104. LCM is the number which is evenly divisible by 8 and 13. From the common multiples, the least common multiple of 8 and 13 can be calculated. The multiples of 8 are (8, 16, 24, 32, 40, 48, ….) and the multiples of 13 are (13, 26, 39, 52, 65, ….) respectively. Division, Prime factorisation and listing of the multiples are the most common methods used to get the LCM value.
Also read: Least common multiple
What is LCM of 8 and 13?
The answer to this question is 104. The LCM of 8 and 13 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8 and 13, is the smallest positive integer 104 which is divisible by both 8 and 13 with no remainder.
How to Find LCM of 8 and 13?
LCM of 8 and 13 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 13 Using Prime Factorisation Method
The prime factorisation of 8 and 13, respectively, is given by:
8 = 2 x 2 x 2 = 2³
13 = 13¹
LCM (8, 13) = 104
LCM of 8 and 13 Using Division Method
We’ll divide the numbers (8, 13) by their prime factors to get the LCM of 8 and 13 using the division method (preferably common). The LCM of 8 and 13 is calculated by multiplying these divisors.
2 | 8 | 13 |
2 | 4 | 13 |
2 | 2 | 13 |
13 | 1 | 13 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (8, 13) = 104
LCM of 8 and 13 Using Listing the Multiples
To calculate the LCM of 8 and 13 by listing out the common multiples, list the multiples as shown below
Multiples of 8 | Multiples of 13 |
8 | 13 |
16 | 26 |
24 | 39 |
32 | 52 |
40 | 65 |
48 | 78 |
56 | 91 |
64 | 104 |
72 | 117 |
80 | 130 |
88 | 143 |
96 | 156 |
104 | 169 |
112 | 182 |
LCM (8, 13) = 104
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Video Lesson on Applications of LCM
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LCM of 8 and 13 Solved Examples
If the product of two numbers is 104, calculate the LCM if the GCD is 1.
Solution:
It is given that
GCD = 1
Product of two numbers = 104
We know that
LCM x GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 104/1
LCM = 104
Hence, the LCM is 104.
Frequently Asked Questions on LCM of 8 and 13
What is the LCM of 8 and 13?
We know that,
Multiples of 8 = 8, 16, 24, 32, 40, 48, ….
Multiples of 13 = 13, 26, 39, 52, 65, ….
The smallest multiple exactly divisible by 8 and 13 is 104.
If the LCM of 8 and 13 is 104, determine the GCF.
LCM x GCF = 8 x 13
Given,
LCM of 8 and 13 is 104
104 x GCF = 104
GCF = 104/104 = 1
What are the methods used to find the LCM of 8 and 13?
The methods used to find the LCM of 8 and 13 are
Division method
Prime Factorisation
Listing the multiples
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