lcm of 6 and 8

LCM of 6 and 8 is 24. The smallest value that divides all the numbers under consideration is called the LCM, or least common multiple, of two or more numbers. So, the LCM of 6 and 8 is the smallest number that can be divided by both 6 and 8 without leaving any remainder.

In this article, we will discuss the concept of LCM and specifically explore its calculation for the numbers 6 and 8.

LCM of 6 and 8 is 24

What is LCM of 6 and 8?

Answer: LCM of 6 and 8 is 24.

LCM of the two numbers is the smallest number that can be divided by both numbers without producing a remainder. We can use variety of techniques, including prime factorization and the listing multiples method, to determine the LCM of 6 and 8.

What is LCM?

Lowest Multiple that can be divided by each of the provided numbers without leaving any remainder is the LCM (Least Common Multiple) of those numbers.

LCM of 6 and 8 Calculator

How to Find LCM of 6 and 8?

There are three methods discussed here to find the LCM of 6 and 8 that are,

• LCM of 6 and 8 by Prime Factorization
• LCM of 6 and 8 by Listing Multiple
• LCM of 6 and 8 by Long Division

LCM of 6 and 8 by Prime Factorization

The prime factors for both 6 and 8 are listed to compute LCM of 6 and 8.

• Prime factors of number 6 = 2¹ × 3¹
• Prime factors of number 8 = 2 × 2 × 2 = 2³

LCM is obtained by multiplying the highest powers of prime factors.

LCM of 6 and 8 = 2 × 2 × 2 × 3 = 24.

Therefore, LCM of 6 and 8 is 24.

LCM of 6 and 8 by Listing Multiples

To get the Least Common Multiple of 6 and 8, you must first start by listing a few multiples of each integer. So, Let’s take a look at the first 10 multiples for 6 and 8:

• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
• Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Here, 24 is the first common multiple of both 6 and 8.

Therefore, LCM of 6 and 8 by listing multiples is 24.

LCM of 6 and 8 by Long Division Method

Using division method, we can find LCM of 6 and 8 by dividing the integers by their prime factors.

Step 1: Find the smallest prime number (2) that is a factor of at least one of the numbers. Whereas, 6 and 8 should be divided according to the ladder arrangement.

Step 2: Now divide 6 and 8 by 2 and write the quotient below it if it is a multiple of 2. Any number not divisible by the prime number should be brought down as it is.

Step 3: Continue this process, until 1 is left in the last row.

LCM of 6 and 8 by Long Division Method

Therefore, the LCM of 6 and 8 by long division method is 2 × 2 × 2 × 3 = 24.

LCM and HCF of 6 and 8

The LCM (Least Common Multiple) of 6 and 8 is 24 and the HCF (Highest Common Factor) of 6 and 8 is 2.

Also, LCM × HCF = Product of Two Numbers

• 6 = 2 × 3
• 8 = 2 × 2 × 2

LCM (6, 8) = 2 × 2 × 2 × 3 = 24

HCF (6, 8) = 2

6 × 8 = LCM (6, 8) × HCF (6, 8)

48 = 24 × 2

48 = 48

Example on LCM of 6 and 8

Example 1: Determine the smallest integer that can be divided exactly by six and eight.

Solution:

LCM is the smallest number that is precisely divisible by 6 and 8.

Multiples of 6 and 8

• Multiples of 6 = 6, 12, 18, 24, 30, 36, 42
• Multiples of 8 = 8, 16, 24, 32, 40, 48, 56

Therefore, LCM of 6 and 8 is 24.

Example 2: Numbers 2 and 24 are GCF and LCM of two numbers respectively. If one number is 6, find the other number.

Solution:

Let ‘x’ be the other number

GCF × LCM = 6 × x

x = (GCF × LCM) / 6

x = (2 × 24) / 6

x = 8

Hence, the other number is 8.

Practice Problems on LCM of 6 and 8

P1: Calculate the LCM of 6 and 8.

P2: Find the LCM of 6 and 8 using prime factorization.

P3: Determine the smallest positive integer that is divisible by both 6 and 8.

P4: If x is the LCM of 6 and 8, what is the value of x?

FAQs on LCM of 6 and 8

What is the Least Common Multiple (LCM) of 6 and 8?

LCM of 6 and 8 is 24.

What is the LCM of 6,8, and 12?

The LCM of 6, 8, and 12 is 24. So, without leaving a leftover, 24 is the smallest number that can be divided by all three numbers.

How do you find the LCM of 6 and 8 by Prime Factorization?

Let’s find the LCM of 6 and 8 by Prime Factorization:

Prime factors of number 6 = 2 × 3

Prime factors of number 8 = 2 × 2 × 2

LCM = 2 × 2 × 2 × 3 = 24.

What are GCF and LCM of 6 and 8?

The GCF of 6 and 8 is 2, and the LCM of 6 and 8 is 24.

What are the Methods to find LCM of 6 and 8?

Methods used to find the LCM of 6 and 8 are:

• Prime Factorization Method
• Long Division Method
• Listing Common Factors