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LCM of 8 and 5

LCM of 8 and 5 is the smallest number among all common multiples of 8 and 5. The first few multiples of 8 and 5 are (8, 16, 24, 32, 40, 48, 56, . . . ) and (5, 10, 15, 20, 25, 30, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 5 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 8 and 5
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 8 and 5?

Answer: LCM of 8 and 5 is 40.

Explanation:

The LCM of two non-zero integers, x(8) and y(5), is the smallest positive integer m(40) that is divisible by both x(8) and y(5) without any remainder.

Methods to Find LCM of 8 and 5

The methods to find the LCM of 8 and 5 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 8 and 5 by Division Method

To calculate the LCM of 8 and 5 by the division method, we will divide the numbers(8, 5) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 5.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 5. Write this prime number(2) on the left of the given numbers(8 and 5), separated as per the ladder arrangement.
Step 2: If any of the given numbers (8, 5) 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 5 is the product of all prime numbers on the left, i.e. LCM(8, 5) by division method = 2 × 2 × 2 × 5 = 40.

LCM of 8 and 5 by Prime Factorization

Prime factorization of 8 and 5 is (2 × 2 × 2) = 2³ and (5) = 5¹ respectively. LCM of 8 and 5 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5¹ = 40.
Hence, the LCM of 8 and 5 by prime factorization is 40.

LCM of 8 and 5 by Listing Multiples

To calculate the LCM of 8 and 5 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, 56, . . . ) and 5 (5, 10, 15, 20, 25, 30, . . . . )
Step 2: The common multiples from the multiples of 8 and 5 are 40, 80, . . .
Step 3: The smallest common multiple of 8 and 5 is 40.

∴ The least common multiple of 8 and 5 = 40.

☛ Also Check:

LCM of 8 and 5 Examples

Example 1: The GCD and LCM of two numbers are 1 and 40 respectively. If one number is 8, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 8 × z
⇒ z = (GCD × LCM)/8
⇒ z = (1 × 40)/8
⇒ z = 5
Therefore, the other number is 5.
Example 2: Verify the relationship between GCF and LCM of 8 and 5.

Solution:

The relation between GCF and LCM of 8 and 5 is given as,
LCM(8, 5) × GCF(8, 5) = Product of 8, 5
Prime factorization of 8 and 5 is given as, 8 = (2 × 2 × 2) = 2³ and 5 = (5) = 5¹
LCM(8, 5) = 40
GCF(8, 5) = 1
LHS = LCM(8, 5) × GCF(8, 5) = 40 × 1 = 40
RHS = Product of 8, 5 = 8 × 5 = 40
⇒ LHS = RHS = 40
Hence, verified.
Example 3: The product of two numbers is 40. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 40
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 40/1
Therefore, the LCM is 40.
The probable combination for the given case is LCM(8, 5) = 40.

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FAQs on LCM of 8 and 5

What is the LCM of 8 and 5?

The LCM of 8 and 5 is 40. To find the LCM (least common multiple) of 8 and 5, we need to find the multiples of 8 and 5 (multiples of 8 = 8, 16, 24, 32 . . . . 40; multiples of 5 = 5, 10, 15, 20 . . . . 40) and choose the smallest multiple that is exactly divisible by 8 and 5, i.e., 40.

What is the Least Perfect Square Divisible by 8 and 5?

The least number divisible by 8 and 5 = LCM(8, 5)
LCM of 8 and 5 = 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 8 and 5 = LCM(8, 5) × 2 × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

What are the Methods to Find LCM of 8 and 5?

The commonly used methods to find the LCM of 8 and 5 are:

Prime Factorization Method
Division Method
Listing Multiples

How to Find the LCM of 8 and 5 by Prime Factorization?

To find the LCM of 8 and 5 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (5 = 5). LCM of 8 and 5 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 5.
⇒ LCM of 8, 5 = 2³ × 5¹ = 40.

If the LCM of 5 and 8 is 40, Find its GCF.

LCM(5, 8) × GCF(5, 8) = 5 × 8
Since the LCM of 5 and 8 = 40
⇒ 40 × GCF(5, 8) = 40
Therefore, the GCF (greatest common factor) = 40/40 = 1.

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