LCM of 21 and 28
2026-02-28 15:49 Diff
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Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 21 and 28. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. In our daily life, we use application of LCM for setting alarms in our clock or coordinating any orders.

What is the LCM of 21 and 28?

How to find the LCM of 21 and 28 ?

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

LCM of 21 and 28 using the Listing Multiples method

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. 

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LCM of 21 and 28 using the Prime Factorization

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

LCM of 21 and 28 using the Division method

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

Common Mistakes and how to avoid them in LCM of 21 and 28

here some common mistake with their solutions are given:

Problem 1

LCM of 21 and b is 84. HCF of the same is 7. Find b.

Okay, lets begin

The following relationship can be used to find the other number b. 


LCM×HCF=Product of the two numbers 


Substituting into the formula: 


84×7 = 21×b


588 = 21b


b= 28
 

Explanation

The above is how we find the other number when the LCM, HCF, and one of the numbers is given.

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Problem 2

Find x such that both 21 and 28 are its factors.

Okay, lets begin

The LCM of 21 and 28 = 84 

Explanation

the smallest number both 21 and 28 divide is the LCM of the numbers itself. All multiples of 84 are factored by 21 and 28. 
 

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Problem 3

Solve for the LCM of 21 and 28 using → LCM(a,b)=a×b/HCF(a,b)

Okay, lets begin

HCF of 21 and 28 → 7 


Applying the values in the formula;

 
LCM(a,b)=a×b/HCF(a,b)


LCM(21,28)=21×28/7


LCM(21,28) = 84
 

Explanation

By applying the formula as above, we can ascertain the LCM of two numbers directly without using the prime factorization or other methods. 
 

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FAQs on LCM of 21 and 28

1.What is the LCM of 12 and 28?

Prime factorization of 12 = 2×2×3


Prime factorization of 28 = 2×2×7


LCM(12,28) = 84 
 

2.What is the LCM of 21,24 and 28?

Prime factorization of 28 = 2×2×7


Prime factorization of 21 = 3×7


Prime factorization of 24 = 2×2×3×2


LCM (21,24,28) = 168
 

3.What is the LCM of 21 and 27?

Prime factorization of 21 = 3×7


Prime factorization of 27 = 3×3×3


LCM (21,27) = 189
 

4.What is the LCM of 14,21 and 28?

Prime factorization of 28 = 2×2×7


Prime factorization of 21 = 3×7


Prime factorization of 14 = 2×7


LCM (14,21,28) = 84
 

5.What is the LCM of 21 and 25?

Prime factorization of 21 = 3×7


Prime factorization of 25= 5×5


LCM(21,25) = 525 
 

Important glossaries for LCM of 21 and 28

  • 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.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.