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LCM of 5 and 13

LCM of 5 and 13 is the smallest number among all common multiples of 5 and 13. The first few multiples of 5 and 13 are (5, 10, 15, 20, . . . ) and (13, 26, 39, 52, 65, 78, 91, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 13 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 5 and 13
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 5 and 13?

Answer: LCM of 5 and 13 is 65.

Explanation:

The LCM of two non-zero integers, x(5) and y(13), is the smallest positive integer m(65) that is divisible by both x(5) and y(13) without any remainder.

Methods to Find LCM of 5 and 13

The methods to find the LCM of 5 and 13 are explained below.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 5 and 13 by Prime Factorization

Prime factorization of 5 and 13 is (5) = 5¹ and (13) = 13¹ respectively. LCM of 5 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 5¹ × 13¹ = 65.
Hence, the LCM of 5 and 13 by prime factorization is 65.

LCM of 5 and 13 by Division Method

To calculate the LCM of 5 and 13 by the division method, we will divide the numbers(5, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 13.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 13. Write this prime number(5) on the left of the given numbers(5 and 13), separated as per the ladder arrangement.
Step 2: If any of the given numbers (5, 13) is a multiple of 5, divide it by 5 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 5 and 13 is the product of all prime numbers on the left, i.e. LCM(5, 13) by division method = 5 × 13 = 65.

LCM of 5 and 13 by Listing Multiples

To calculate the LCM of 5 and 13 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 5 (5, 10, 15, 20, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )
Step 2: The common multiples from the multiples of 5 and 13 are 65, 130, . . .
Step 3: The smallest common multiple of 5 and 13 is 65.

∴ The least common multiple of 5 and 13 = 65.

☛ Also Check:

LCM of 5 and 13 Examples

Example 1: The product of two numbers is 65. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 65
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 65/1
Therefore, the LCM is 65.
The probable combination for the given case is LCM(5, 13) = 65.
Example 2: The GCD and LCM of two numbers are 1 and 65 respectively. If one number is 5, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 5 × b
⇒ b = (GCD × LCM)/5
⇒ b = (1 × 65)/5
⇒ b = 13
Therefore, the other number is 13.
Example 3: Verify the relationship between GCF and LCM of 5 and 13.

Solution:

The relation between GCF and LCM of 5 and 13 is given as,
LCM(5, 13) × GCF(5, 13) = Product of 5, 13
Prime factorization of 5 and 13 is given as, 5 = (5) = 5¹ and 13 = (13) = 13¹
LCM(5, 13) = 65
GCF(5, 13) = 1
LHS = LCM(5, 13) × GCF(5, 13) = 65 × 1 = 65
RHS = Product of 5, 13 = 5 × 13 = 65
⇒ LHS = RHS = 65
Hence, verified.

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FAQs on LCM of 5 and 13

What is the LCM of 5 and 13?

The LCM of 5 and 13 is 65. To find the LCM (least common multiple) of 5 and 13, we need to find the multiples of 5 and 13 (multiples of 5 = 5, 10, 15, 20 . . . . 65; multiples of 13 = 13, 26, 39, 52 . . . . 65) and choose the smallest multiple that is exactly divisible by 5 and 13, i.e., 65.

What is the Least Perfect Square Divisible by 5 and 13?

The least number divisible by 5 and 13 = LCM(5, 13)
LCM of 5 and 13 = 5 × 13 [Incomplete pair(s): 5, 13]
⇒ Least perfect square divisible by each 5 and 13 = LCM(5, 13) × 5 × 13 = 4225 [Square root of 4225 = √4225 = ±65]
Therefore, 4225 is the required number.

Which of the following is the LCM of 5 and 13? 65, 28, 2, 32

The value of LCM of 5, 13 is the smallest common multiple of 5 and 13. The number satisfying the given condition is 65.

How to Find the LCM of 5 and 13 by Prime Factorization?

To find the LCM of 5 and 13 using prime factorization, we will find the prime factors, (5 = 5) and (13 = 13). LCM of 5 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 5 and 13.
⇒ LCM of 5, 13 = 5¹ × 13¹ = 65.

If the LCM of 13 and 5 is 65, Find its GCF.

LCM(13, 5) × GCF(13, 5) = 13 × 5
Since the LCM of 13 and 5 = 65
⇒ 65 × GCF(13, 5) = 65
Therefore, the GCF = 65/65 = 1.

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