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LCM of 2 and 8

LCM of 2 and 8 is the smallest number among all common multiples of 2 and 8. The first few multiples of 2 and 8 are (2, 4, 6, 8, 10, 12, 14, . . . ) and (8, 16, 24, 32, 40, 48, 56, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 8 - by listing multiples, by prime factorization, and by division method.

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

What is the LCM of 2 and 8?

Answer: LCM of 2 and 8 is 8.

Explanation:

The LCM of two non-zero integers, x(2) and y(8), is the smallest positive integer m(8) that is divisible by both x(2) and y(8) without any remainder.

Methods to Find LCM of 2 and 8

The methods to find the LCM of 2 and 8 are explained below.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 2 and 8 by Prime Factorization

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

LCM of 2 and 8 by Division Method

To calculate the LCM of 2 and 8 by the division method, we will divide the numbers(2, 8) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 8.

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

LCM of 2 and 8 by Listing Multiples

To calculate the LCM of 2 and 8 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, 12, 14, . . . ) and 8 (8, 16, 24, 32, 40, 48, 56, . . . . )
Step 2: The common multiples from the multiples of 2 and 8 are 8, 16, . . .
Step 3: The smallest common multiple of 2 and 8 is 8.

∴ The least common multiple of 2 and 8 = 8.

☛ Also Check:

LCM of 2 and 8 Examples

Example 1: The product of two numbers is 16. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 16
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 16/2
Therefore, the LCM is 8.
The probable combination for the given case is LCM(2, 8) = 8.
Example 2: Find the smallest number that is divisible by 2 and 8 exactly.

Solution:

The smallest number that is divisible by 2 and 8 exactly is their LCM.
⇒ Multiples of 2 and 8:
- Multiples of 2 = 2, 4, 6, 8, 10, . . . .
- Multiples of 8 = 8, 16, 24, 32, 40, . . . .
Therefore, the LCM of 2 and 8 is 8.
Example 3: Verify the relationship between GCF and LCM of 2 and 8.

Solution:

The relation between GCF and LCM of 2 and 8 is given as,
LCM(2, 8) × GCF(2, 8) = Product of 2, 8
Prime factorization of 2 and 8 is given as, 2 = (2) = 2¹ and 8 = (2 × 2 × 2) = 2³
LCM(2, 8) = 8
GCF(2, 8) = 2
LHS = LCM(2, 8) × GCF(2, 8) = 8 × 2 = 16
RHS = Product of 2, 8 = 2 × 8 = 16
⇒ LHS = RHS = 16
Hence, verified.

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FAQs on LCM of 2 and 8

What is the LCM of 2 and 8?

The LCM of 2 and 8 is 8. To find the least common multiple (LCM) of 2 and 8, we need to find the multiples of 2 and 8 (multiples of 2 = 2, 4, 6, 8; multiples of 8 = 8, 16, 24, 32) and choose the smallest multiple that is exactly divisible by 2 and 8, i.e., 8.

What is the Relation Between GCF and LCM of 2, 8?

The following equation can be used to express the relation between GCF and LCM of 2 and 8, i.e. GCF × LCM = 2 × 8.

How to Find the LCM of 2 and 8 by Prime Factorization?

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

Which of the following is the LCM of 2 and 8? 12, 8, 20, 15

The value of LCM of 2, 8 is the smallest common multiple of 2 and 8. The number satisfying the given condition is 8.

If the LCM of 8 and 2 is 8, Find its GCF.

LCM(8, 2) × GCF(8, 2) = 8 × 2
Since the LCM of 8 and 2 = 8
⇒ 8 × GCF(8, 2) = 16
Therefore, the greatest common factor (GCF) = 16/8 = 2.

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