LCM of 8 and 13
LCM of 8 and 13 is the smallest number among all common multiples of 8 and 13. The first few multiples of 8 and 13 are (8, 16, 24, 32, 40, 48, . . . ) and (13, 26, 39, 52, 65, 78, 91, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 13  by prime factorization, by listing multiples, and by division method.
1.  LCM of 8 and 13 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 8 and 13?
Answer: LCM of 8 and 13 is 104.
Explanation:
The LCM of two nonzero integers, x(8) and y(13), is the smallest positive integer m(104) that is divisible by both x(8) and y(13) without any remainder.
Methods to Find LCM of 8 and 13
The methods to find the LCM of 8 and 13 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 8 and 13 by Prime Factorization
Prime factorization of 8 and 13 is (2 × 2 × 2) = 2^{3} and (13) = 13^{1} respectively. LCM of 8 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 13^{1} = 104.
Hence, the LCM of 8 and 13 by prime factorization is 104.
LCM of 8 and 13 by Division Method
To calculate the LCM of 8 and 13 by the division method, we will divide the numbers(8, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 13.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 13. Write this prime number(2) on the left of the given numbers(8 and 13), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (8, 13) 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 8 and 13 is the product of all prime numbers on the left, i.e. LCM(8, 13) by division method = 2 × 2 × 2 × 13 = 104.
LCM of 8 and 13 by Listing Multiples
To calculate the LCM of 8 and 13 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )
 Step 2: The common multiples from the multiples of 8 and 13 are 104, 208, . . .
 Step 3: The smallest common multiple of 8 and 13 is 104.
∴ The least common multiple of 8 and 13 = 104.
☛ Also Check:
 LCM of 5 and 25  25
 LCM of 16 and 28  112
 LCM of 4, 5 and 10  20
 LCM of 2, 5 and 7  70
 LCM of 8, 9 and 10  360
 LCM of 1 and 2  2
 LCM of 5, 10, 15 and 30  30
LCM of 8 and 13 Examples

Example 1: The product of two numbers is 104. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 104
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 104/1
Therefore, the LCM is 104.
The probable combination for the given case is LCM(8, 13) = 104. 
Example 2: Verify the relationship between GCF and LCM of 8 and 13.
Solution:
The relation between GCF and LCM of 8 and 13 is given as,
LCM(8, 13) × GCF(8, 13) = Product of 8, 13
Prime factorization of 8 and 13 is given as, 8 = (2 × 2 × 2) = 2^{3} and 13 = (13) = 13^{1}
LCM(8, 13) = 104
GCF(8, 13) = 1
LHS = LCM(8, 13) × GCF(8, 13) = 104 × 1 = 104
RHS = Product of 8, 13 = 8 × 13 = 104
⇒ LHS = RHS = 104
Hence, verified. 
Example 3: Find the smallest number that is divisible by 8 and 13 exactly.
Solution:
The smallest number that is divisible by 8 and 13 exactly is their LCM.
⇒ Multiples of 8 and 13: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, . . . .
 Multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, . . . .
Therefore, the LCM of 8 and 13 is 104.
FAQs on LCM of 8 and 13
What is the LCM of 8 and 13?
The LCM of 8 and 13 is 104. To find the least common multiple (LCM) of 8 and 13, we need to find the multiples of 8 and 13 (multiples of 8 = 8, 16, 24, 32 . . . . 104; multiples of 13 = 13, 26, 39, 52 . . . . 104) and choose the smallest multiple that is exactly divisible by 8 and 13, i.e., 104.
What is the Least Perfect Square Divisible by 8 and 13?
The least number divisible by 8 and 13 = LCM(8, 13)
LCM of 8 and 13 = 2 × 2 × 2 × 13 [Incomplete pair(s): 2, 13]
⇒ Least perfect square divisible by each 8 and 13 = LCM(8, 13) × 2 × 13 = 2704 [Square root of 2704 = √2704 = ±52]
Therefore, 2704 is the required number.
If the LCM of 13 and 8 is 104, Find its GCF.
LCM(13, 8) × GCF(13, 8) = 13 × 8
Since the LCM of 13 and 8 = 104
⇒ 104 × GCF(13, 8) = 104
Therefore, the greatest common factor = 104/104 = 1.
How to Find the LCM of 8 and 13 by Prime Factorization?
To find the LCM of 8 and 13 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (13 = 13). LCM of 8 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 13.
⇒ LCM of 8, 13 = 2^{3} × 13^{1} = 104.
What is the Relation Between GCF and LCM of 8, 13?
The following equation can be used to express the relation between GCF and LCM of 8 and 13, i.e. GCF × LCM = 8 × 13.
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