LCM of 30 and 42
2026-02-28 13:47 Diff
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Last updated on August 5, 2025

In this article, we will learn how to learn LCM by using different methods and learn to apply the LCM. We can simplify mathematical calculations and efficiently solve the problems by learning the LCM

What is the LCM of 30 and 42?

How to find the LCM of 30 and 42?

We can find the LCM using the listing method, prime factorization method and division method as explained below; 
 

LCM of 30 and 42 using the Listing multiples method

The LCM of 30 and 42 can be found using the following steps


Step 1: Write down the multiples of each number: 


Multiples of 30–30,60,90,120,150,180,210,…


Multiples of 42–42,84,126,168,210,…


Step 2: Pick the smallest multiple from the multiples of 30 and 42. 


The LCM of 30 and 42 = 210
 

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LCM of 30 and 42 using the Prime Factorization

The prime factors of the given numbers are written, and the highest power of the prime factors is multiplied to get the LCM.


Step 1:  Find the prime factors of the numbers:


30= 3×5×2


42 = 2×3×7


Step 2 : Multiply the highest power of each factor to get the LCM. 


LCM (30,42) = 210

LCM of 30 and 42 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 :A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’. Carry forward the numbers not divisible by the previously picked prime number.

    Step 3 :The LCM of the numbers is the product of the prime numbers in the first column, i.e, LCM (30,42) = 210

Common Mistakes and how to avoid them in LCM of 30 and 42

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 30 and 42 make a note while practicing.
 

Problem 1

Verify LCM(a,b)×HCF(a,b)=a×b, where a= 30 and b=42.

Okay, lets begin

LCM of 30,42; 


Prime factorize the numbers; 


30= 3×5×2


42 =  2×3×7


LCM (30,42) = 210


HCF of 30,42; 


Factors of 30–1,2,3,5,6,10,15,30


Factors of 42–1,2,3,6,7,21,42


HCF(30,42)= 6


Verifying the formula; 


LCM(a,b)×HCF(a,b)=a×b


210×6=30×42


1260 =1260
 

Explanation

The LHS is equal to the RHS, hence the relationship as given in the formula stands true. 
 

Well explained 👍

Problem 2

The LCM of 30 and x is 210. HCF of 30 and x is 6. Find x.

Okay, lets begin

Given;


LCM(30,x) = 210


HCF(30,x) = 6 


To find x, we use →LCM(a,b)=a×b/HCF(a,b) 


We now solve for x, 


30×x/6 = 210 


30×x = 210×6


30×x = 1260 


x = 1260/30 = 42
 

Explanation

The above is how we ascertain the value of x, which is 42. 
 

Well explained 👍

Problem 3

Find x where, LCM (32,x)=210 and HCF(32,x)=6.

Okay, lets begin

x= 40
 

Explanation

The only number that satisfies both the conditions LCM (32,x)=210 and HCF(32,x)=6 is 42. HCF of 30 and 42 is 6 and the LCM of the same is 210. 
 

Well explained 👍

FAQ’s on LCM of 30 and 42

1.What is the LCM of 35 and 42?

Prime factorize the numbers;


35 = 3×7


42 =  2×3×7


LCM (35,42) = 210
 

2.What are the factors of 30 and 42?

Factors of 30–1,2,3,5,6,10,15,30


Factors of 42–1,2,3,6,7,21,42


Common factors of 30 and 42–1,2,3,6
 

3.What is the LCM of 26 and 39?

Prime factorize the numbers;


26 = 2×13


39 = 13×3


LCM(26,39) = 78
 

4. What is the LCM of 30,42 and 48?

Prime factorize the numbers;


30 = 2×3×5


 42 = 2×3×7


48 = 2×2×2×2×3


LCM (30,32,48) = 1680
 

5.What is the LCM of 30 and 48?

Prime factorize the numbers;


30 = 2×3×5


48 = 2×2×2×2×3


LCM(30,48) = 240
 

Important glossaries for the LCM of 30 and 42

  • Multiple — It is a product of a number and any natural integer. So for 30,both 3,2 and 5 are the multiples.
  • Prime Factor — It is a prime number that one gets after factorization of any given number. Like for 30, 2,3,5,6,15 and 30 are prime factors as they can be divided by 1 or the number itself.
  • Prime Factorization — It is a process of dividing the number into prime factors.
  • Co-prime numbers — These are the positive integers where both the numbers can be divided only by 1. 
  • Fraction — It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 30/5 ,30 is the numerator and 5 is the denominator. Proper fraction is where numerator is always lesser than denominator.
     

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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.