LCM of 8 and 12

The LCM of 8 and 12 is the smallest positive integer, a multiple of both numbers.

 

By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.  

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

To ascertain the LCM, list the multiples of the integers until a common multiple is found. 

Steps:

1. Writedown the multiples of each number: 

Multiples of 8 = 8,16,24,32…
Multiples of 12 = 12,24,36… 

2. Ascertain the smallest multiple from the listed multiples of 8 and 12. 

The LCM (Least common multiple) of 8 and 12 is 24. i.e., 24 is divisible by 8 and 12 with no reminder.
 

This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.

Steps: 

1. Find the prime factors of the numbers:

 

• Prime factorization of 8 = 2×2×2
• Prime factorization of 12 = 2×2×3

  

2.  Take the highest power of each prime factor:

= 2,2,2,3

3. Multiply the ascertained factors to get the LCM: 

LCM (8,12) = 2×2×2×3 = 24

The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 

 

Steps:

 

1. Write down the numbers in a row;

 

 

2. Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. 

 

 

3. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

 

 

4. The LCM of the numbers is the product of the prime numbers in the first column, i.e., 

 

2×2×2×3= 24 

 

LCM (8,12) = 24

• Multiple: A number and any integer multiplied. 

 

• Prime Factor: A natural number (other than 1) that has factors that are one and itself.

 

• Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 

 

• Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 

 

• Relatively Prime Numbers: Numbers that have no common factors other than 1.

 

• Fraction: A representation of a part of a whole.