How To Find LCM of 6 and 8? | Listing, Division, and Prime Factorization Method

Question 1: What is the least possible number which is divisible by 6 and 8?
Solution:
There are three methods using which you can find the least possible number which is divisible by 6 and 8.
We will find it using the division method. First, we will find the smallest prime number which is divisible by either 6 or 8. If any of the numbers among 6 and 8 is not divisible by the respective prime number, we will write that number in the next row just below it and proceed further. We will continue dividing the numbers obtained after each step by the prime numbers until we get the result as 1 in the entire row. We will multiply all the prime numbers and the final result will be the LCM of 6 and 8.

So, LCM of 6 and 8 = 2 * 2 * 2 * 3 = 24

Question 2: What is the LCM of 6, 8, and 12?
Solution:
We will find the LCM of 6, 8, and 12 using the prime factorization method:
To find the LCM of 6, 8, and 12 using the prime factorization method, first, we will find the prime factors of 6, 8, and 12 using the repeated division method. Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power. The final result after multiplication will be the LCM of 6, 8, and 12.

• Prime factorization of 6 can be expressed as 2 * 3 = 2¹ * 3¹
• Prime factorization of 8 can be expressed as 2 * 2 * 2 = 2¹ * 2¹ * 2¹ = 2³
• Prime factorization of 12 can be expressed as 2 * 2 * 3 = 2¹ * 2¹ * 3¹ = 2² * 3¹

So, the LCM of 6, 8, and 12 = 2³ * 3¹ = 2 * 2 * 2 * 3 = 24

Question 3: Find the LCM of 6 and 8 using the listing method.
Solution:
To find the LCM of 6 and 8 using the listing method, first, we will write down the first few multiples of 6 and 8 separately. Out of all the multiples of 6 and 8, we will focus on the multiples which are common to both numbers.
Then, out of all the common multiples, we will take out the smallest common multiple. That will be the LCM of 6 and 8.

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

Here, it is clear that the least common multiple is 24. So, the LCM of 6 and 8 is 24.

Question 4: If the LCM of two numbers is 24, HCF is 2, and one of the numbers is 6, find the other number.
Solution:
As we know,
the product of two numbers = LCM * HCF
It is given that,
one of the numbers = 6, LCM = 24, and HCF = 2
Let the other number be x.
So, 6 * x = 24 * 2
x = (24 * 2) / 6
x = 48 / 6
x = 8
Hence, the other number is 8.

Question 5: Find the LCM of 6 and 8 using the prime factorization method.
Solution:
To find the LCM of 6 and 8 using the prime factorization method, first, we will find the prime factors of 6 and 8 using the repeated division method. Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power. The final result after multiplication will be the LCM of 6 and 8.

• Prime factorization of 6 can be expressed as 2 * 3 = 2¹ * 3¹
• Prime factorization of 8 can be expressed as 2 * 2 * 2 = 2¹ * 2¹ * 2¹ = 2³

So, the LCM of 6 and 8 = 2³ * 3¹ = 2 * 2 * 2 * 3 = 24

Are the LCM of 6 and 8 the same as the LCM of 6, 8, and 12?
LCM of 6 and 8 is 24 and LCM of 6, 8, and 12 is also 24. So, the LCM of 6 and 8 are the same as the LCM of 6, 8, and 12.

What is the LCM of 6 and 8?
LCM of 6 and 8 is 24.

Is 48 also considered as the LCM of 6 and 8?
No, 48 is not considered as the LCM of 6 and 8. 48 is a common multiple of 6 and 8. But, it is not the least common number which is divisible by 6 and 8, and while finding the LCM, you must focus on the lowest common number. So, 24 is the lowest common number divisible by 6 and 8.

Are LCM and HCF of 6 and 8 the same?
LCM of 6 and 8 is 24 and HCF of 6 and 8 is 2. So, LCM and HCF of 6 and 8 are not the same.

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

There are 3 major methods for finding the LCM of 6 and 8:

• Listing Method 
• Prime Factorization Method
• Division Method