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LCM of 8 and 10

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

1.	LCM of 8 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 8 and 10?

Answer: LCM of 8 and 10 is 40.

Explanation:

The LCM of two non-zero integers, x(8) and y(10), is the smallest positive integer m(40) that is divisible by both x(8) and y(10) without any remainder.

Methods to Find LCM of 8 and 10

Let's look at the different methods for finding the LCM of 8 and 10.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 8 and 10 by Prime Factorization

Prime factorization of 8 and 10 is (2 × 2 × 2) = 2³ and (2 × 5) = 2¹ × 5¹ respectively. LCM of 8 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5¹ = 40.
Hence, the LCM of 8 and 10 by prime factorization is 40.

LCM of 8 and 10 by Listing Multiples

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

∴ The least common multiple of 8 and 10 = 40.

LCM of 8 and 10 by Division Method

To calculate the LCM of 8 and 10 by the division method, we will divide the numbers(8, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 10.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 10. Write this prime number(2) on the left of the given numbers(8 and 10), separated as per the ladder arrangement.
Step 2: If any of the given numbers (8, 10) 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 10 is the product of all prime numbers on the left, i.e. LCM(8, 10) by division method = 2 × 2 × 2 × 5 = 40.

☛ Also Check:

LCM of 8 and 10 Examples

Example 1: Verify the relationship between GCF and LCM of 8 and 10.

Solution:

The relation between GCF and LCM of 8 and 10 is given as,
LCM(8, 10) × GCF(8, 10) = Product of 8, 10
Prime factorization of 8 and 10 is given as, 8 = (2 × 2 × 2) = 2³ and 10 = (2 × 5) = 2¹ × 5¹
LCM(8, 10) = 40
GCF(8, 10) = 2
LHS = LCM(8, 10) × GCF(8, 10) = 40 × 2 = 80
RHS = Product of 8, 10 = 8 × 10 = 80
⇒ LHS = RHS = 80
Hence, verified.
Example 2: The product of two numbers is 80. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 80
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 80/2
Therefore, the LCM is 40.
The probable combination for the given case is LCM(8, 10) = 40.
Example 3: The GCD and LCM of two numbers are 2 and 40 respectively. If one number is 10, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 10 × a
⇒ a = (GCD × LCM)/10
⇒ a = (2 × 40)/10
⇒ a = 8
Therefore, the other number is 8.

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FAQs on LCM of 8 and 10

What is the LCM of 8 and 10?

The LCM of 8 and 10 is 40. To find the least common multiple of 8 and 10, we need to find the multiples of 8 and 10 (multiples of 8 = 8, 16, 24, 32 . . . . 40; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 8 and 10, i.e., 40.

What is the Relation Between GCF and LCM of 8, 10?

The following equation can be used to express the relation between GCF and LCM of 8 and 10, i.e. GCF × LCM = 8 × 10.

If the LCM of 10 and 8 is 40, Find its GCF.

LCM(10, 8) × GCF(10, 8) = 10 × 8
Since the LCM of 10 and 8 = 40
⇒ 40 × GCF(10, 8) = 80
Therefore, the greatest common factor (GCF) = 80/40 = 2.

What is the Least Perfect Square Divisible by 8 and 10?

The least number divisible by 8 and 10 = LCM(8, 10)
LCM of 8 and 10 = 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 8 and 10 = LCM(8, 10) × 2 × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

Which of the following is the LCM of 8 and 10? 36, 40, 35, 3

The value of LCM of 8, 10 is the smallest common multiple of 8 and 10. The number satisfying the given condition is 40.

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