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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 non-zero 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) = 3² and (13) = 13¹ respectively. LCM of 9 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 13¹ = 117.
Hence, the LCM of 9 and 13 by prime factorization is 117.

☛ Also Check:

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) = 3² and 13 = (13) = 13¹
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.

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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 = 3² × 13¹ = 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

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