LCM of 9 and 13
LCM of 9 and 13 is the smallest number among all common multiples of 9 and 13. The first few multiples of 9 and 13 are (9, 18, 27, 36, 45, 54, . . . ) and (13, 26, 39, 52, 65, 78, 91, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 13  by listing multiples, by division method, and by prime factorization.
1.  LCM of 9 and 13 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 9 and 13?
Answer: LCM of 9 and 13 is 117.
Explanation:
The LCM of two nonzero integers, x(9) and y(13), is the smallest positive integer m(117) that is divisible by both x(9) and y(13) without any remainder.
Methods to Find LCM of 9 and 13
Let's look at the different methods for finding the LCM of 9 and 13.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 9 and 13 by Listing Multiples
To calculate the LCM of 9 and 13 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )
 Step 2: The common multiples from the multiples of 9 and 13 are 117, 234, . . .
 Step 3: The smallest common multiple of 9 and 13 is 117.
∴ The least common multiple of 9 and 13 = 117.
LCM of 9 and 13 by Division Method
To calculate the LCM of 9 and 13 by the division method, we will divide the numbers(9, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 13.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 13. Write this prime number(3) on the left of the given numbers(9 and 13), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (9, 13) is a multiple of 3, divide it by 3 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 9 and 13 is the product of all prime numbers on the left, i.e. LCM(9, 13) by division method = 3 × 3 × 13 = 117.
LCM of 9 and 13 by Prime Factorization
Prime factorization of 9 and 13 is (3 × 3) = 3^{2} and (13) = 13^{1} respectively. LCM of 9 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{2} × 13^{1} = 117.
Hence, the LCM of 9 and 13 by prime factorization is 117.
☛ Also Check:
 LCM of 18 and 28  252
 LCM of 9 and 27  27
 LCM of 5 and 9  45
 LCM of 2, 5 and 6  30
 LCM of 2601 and 2616  2268072
 LCM of 28 and 70  140
 LCM of 11 and 22  22
LCM of 9 and 13 Examples

Example 1: The product of two numbers is 117. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 117
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 117/1
Therefore, the LCM is 117.
The probable combination for the given case is LCM(9, 13) = 117. 
Example 2: The GCD and LCM of two numbers are 1 and 117 respectively. If one number is 13, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 13 × p
⇒ p = (GCD × LCM)/13
⇒ p = (1 × 117)/13
⇒ p = 9
Therefore, the other number is 9. 
Example 3: Verify the relationship between GCF and LCM of 9 and 13.
Solution:
The relation between GCF and LCM of 9 and 13 is given as,
LCM(9, 13) × GCF(9, 13) = Product of 9, 13
Prime factorization of 9 and 13 is given as, 9 = (3 × 3) = 3^{2} and 13 = (13) = 13^{1}
LCM(9, 13) = 117
GCF(9, 13) = 1
LHS = LCM(9, 13) × GCF(9, 13) = 117 × 1 = 117
RHS = Product of 9, 13 = 9 × 13 = 117
⇒ LHS = RHS = 117
Hence, verified.
FAQs on LCM of 9 and 13
What is the LCM of 9 and 13?
The LCM of 9 and 13 is 117. To find the least common multiple of 9 and 13, we need to find the multiples of 9 and 13 (multiples of 9 = 9, 18, 27, 36 . . . . 117; multiples of 13 = 13, 26, 39, 52 . . . . 117) and choose the smallest multiple that is exactly divisible by 9 and 13, i.e., 117.
Which of the following is the LCM of 9 and 13? 32, 5, 117, 11
The value of LCM of 9, 13 is the smallest common multiple of 9 and 13. The number satisfying the given condition is 117.
How to Find the LCM of 9 and 13 by Prime Factorization?
To find the LCM of 9 and 13 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (13 = 13). LCM of 9 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 13.
⇒ LCM of 9, 13 = 3^{2} × 13^{1} = 117.
If the LCM of 13 and 9 is 117, Find its GCF.
LCM(13, 9) × GCF(13, 9) = 13 × 9
Since the LCM of 13 and 9 = 117
⇒ 117 × GCF(13, 9) = 117
Therefore, the GCF (greatest common factor) = 117/117 = 1.
What are the Methods to Find LCM of 9 and 13?
The commonly used methods to find the LCM of 9 and 13 are:
 Division Method
 Listing Multiples
 Prime Factorization Method