LCM of 21 and 28

The LCM of 21 and 28 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations 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; 
 

The LCM of 21 and 28 can be found using the following steps;

Step 1: Write down the multiples of each number:

 
Multiples of 21 = 21,42,63,84,105,126,147,168,…

Multiples of 28 = 28,56,84,112,140,168,196,…

Step 2: Ascertain the smallest multiple from the listed multiples of 21 and 28. 

The LCM (The Least common multiple) of 21 and 28 is 84, i.e.,84 is divisible by 21 and 28 leaving no reminders. 

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Step 1: Find the prime factors of the numbers:

Prime factorization of 21 = 3×7

Prime factorization of 28  =  2×2×7

Step 2:Take the highest power of each prime factor:

Step 3: Multiply the ascertained factors to get the LCM: 

LCM (21,28) = 84

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

Step 1: Write down the numbers in a row;

Step 2:Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers has not been divisible previously.
   
Step 3:The LCM of the numbers is the product of the prime numbers in the first column, i.e, 

LCM (21,28) = 84

• 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.