How to Find LCM of 8 and 12 By Different Methods – Mindspark

LCM of 8 and 12 

LCM of 8 and 12 is the smallest common multiple of 8 and 12. We have the following four methods to find the LCM of 8 and 12: 

• Listing Multiples
• Prime Factorization Method
• Division Method or Ladder Method
• HCF Method

Listing Multiple Method

In this method, we will list the multiples of 8 and 12 until we find the first common multiple.

Multiples of 8 will be 8, 16, 24, 32, 40, 48 etc.

Multiples of 12 will be: 12, 24, 36, 48, 60, 72 etc.

Here, the number 24 (Bold ) is the first common multiple of both 8 and 12. So, the LCM of 8, 12 is 24.

Prime Factorization Method

In this find, we will list the prime factors of both numbers.

Prime factorization of: 

8 = 2 × 2 × 2

12 = 2 × 2 × 3

Now List all the prime numbers found as they occur most times for any given number. 

The occurrence of Numbers:

2: three times

3: one time

Now, multiply the list of prime factors together to find the least common multiple (LCM).

So, the LCM of 8,12 = 2 × 2 × 2 × 3 = 24

Division/Ladder Method

Write down both the numbers (8 and 12) in the first row. 

Begin with the Lowest Prime Number (2). If the numbers are not divisible by 2, we use the next prime number, i.e. 3. Divide the rows with 2 that evenly divides at least one of the numbers, and write the result into the next row.

If any number is not divisible, write it down as it is. 

Keep dividing, as explained earlier, till the last row is 1.

Now Multiply the prime numbers in the first column.

So the required LCM will be 2 × 2 × 2 × 3 = 24.

HCF Method

The formula used to find the LCM by this method is:

L C M=\frac{a \times b} {H C F(a,b)} 

HCF of 8 and 12 – 

8 = 2 × 2 × 2

12 = 2 × 2 × 3

2 × 2 is common in the prime factorization of 8 and 12.

So, HCF = 2×2 = 4

Now applying the value in the formula 

Required LCM  =8 \times\frac{12}{4}=24

Examples

1. Find the smallest number that is wholly divisible by 8 and 12.

The smallest number completely divisible by 8 and 12 will be their LCM.

Multiples of 8 will be: 8, 16, 24, 32, 40, 48 etc.

Multiples of 12 will be: 12, 24, 36, 48, 60, 72 etc.

So the required LCM = smallest number completely divisible by 8 and 12 = 24

2. If the LCM of the numbers 8 and 12 is 24, Find their HCF.

As per the property of HCF and LCM of two numbers, 

(LCM × HCF) = Product of the numbers

Given that LCM of 12 and 8 = 24

So, 24 × HCF = 96

HCF = 96/24 = 4