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Last updated on May 26th, 2025

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LCM of 36 and 42

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The meaning of least common factor (LCM) is to find the smallest number that divides any two integers evenly. LCM is used mainly in fractions to find a common number for both the integers. We use LCM for solving problems, lining up cycles or even synchronizing of events, also to schedule tasks in everyday life.

LCM of 36 and 42 for Bahraini Students
Professor Greenline from BrightChamps

What is the LCM of 36 and 42?

We use LCM of 36 and 42 to find  the smallest number that divides both the numbers equally.  The smallest positive number is the number that divides both numbers equally, is 252 without leaving any remainder. LCM is used mainly in fractions to find a common number for both the integers.
 

Professor Greenline from BrightChamps

How to find the LCM of 36 and 42?

The LCM of 36 and 42 can be found by the following methods like division method, listing multiples, prime factorization.
 

Professor Greenline from BrightChamps

LCM of 36 and 42 using Division method:

In division method, we divide both the numbers, we begin with dividing side by side the smallest number. We continue dividing until we get a common number that divides both the numbers equally. It makes it easier for the children to focus on prime factors and identify them.

 

  • 2 divides 36 and 42

 

  • 3 divides 18 and 21

 

  • 6 divides 6 

 

  • 7 divides 7

 

Now multiply the divisors : 2×3×6×7=252 which is the LCM.

Professor Greenline from BrightChamps

LCM of 36 and 42 using Listing multiples:

Step 1:Start by listing multiples of both the numbers separately:


Multiples of 36 are 36,72,108,144,180,216,252,288,324,360…..


Multiples of 42 are 42,84,126,168,210,252,294,336,378…..

 

Step 2:The least common factor from the list is 252. Therefore, the LCM of 36 and 42 is 252.

Professor Greenline from BrightChamps

LCM of 36 and 42 using Prime factorization:

Step 1:We part both the numbers unto factors:


Factor of 36: 22×32


Factors of 42: 3×2x7

 

Step 2:Take the powers of both the numbers and multiply together:


LCM=22x32x7=252.
 

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in LCM of 36 and 42

 While solving problems based on the LCM of 36 and 42, children fail to understand few concepts, to give an idea of the mistakes,given below are a few mistakes and solutions of how to avoid them:
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Stopping the division method way too soon.
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students sometimes stop dividing very soon, when they are not able to divide both the numbers with the same number. For example, we can divide14 by 2, but 15 isn't divisible by 2. To continue the dividing method until all the factors are found. The students should continue dividing until they find the common number that divides both the integers.
 

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LCM of 36 and 42 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Find the LCM of 36 and x if the LCM is 252. What is the value of x?

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x=7.

Explanation

LCM(36,x)=252


Prime factors of 36: 22  × 32


252=22 x 32 × 7


Therefore, x must include 7.


x=7.
 

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Max, the Girl Character from BrightChamps

Problem 2

The LCM of y and 42 is 126. Find the value of y.

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y  = 18

Explanation

 LCM(y,42)=126


Prime factors of 42: 2×3x7.


126=2. × 32.× 7


y=3 × 42/7 =18.
 

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Max, the Girl Character from BrightChamps

Problem 3

If the GCD of 36 and 42 is 6, verify the relationship LCM (36,42) x GCD (36,42)=36 × 42.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

GCD(36,42)=6


LCM(36,42)=(36 × 42)/6 =252


Verify : 252 × 6= 36 × 42 =1512
 

Explanation

value of both is equal to 1512

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

If the LCM of two numbers a and b is given by LCM(a, b)=k, find k if a=36 and b=42.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

k=252.
 

Explanation

LCM(36,42)=252


Thus, k=252.
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find two numbers such that their LCM is 252 and one of them is 36.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

22 × 32 to 252

 

= 22 × 32 x7.

Explanation

The other number is 7.
 

Max from BrightChamps Praising Clear Math Explanations
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FAQs on LCM of 36 and 42

1.What is the GCF of 36 and 42?

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2.What is the LCM of 35 and 36?

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3. Write the LCM of 36,42, and 72?

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4.Write nine hundred and fifty thousand in numbers?

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5.What is LCM of 36?

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6.How can children in Bahrain use numbers in everyday life to understand LCM of 36 and 42?

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7.What are some fun ways kids in Bahrain can practice LCM of 36 and 42 with numbers?

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8.What role do numbers and LCM of 36 and 42 play in helping children in Bahrain develop problem-solving skills?

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9.How can families in Bahrain create number-rich environments to improve LCM of 36 and 42 skills?

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Professor Greenline from BrightChamps

Important glossaries on the LCM of 36 and 42

  • Prime Factor: A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.

 

  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2x7.

 

  • Co-prime numbers: numbers which have the only positive divisor of them both as 1. For example, 6 and 7.


 


 

Professor Greenline from BrightChamps

About BrightChamps in Bahrain

At BrightChamps, numbers are more than just digits—they open doors to countless opportunities! We assist children across Bahrain in mastering vital math skills, focusing today on the LCM of 36 and 42 with special focus on understanding the LCM—in a way that’s lively, enjoyable, and easy to understand. Whether your child is working out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, tracking scores at local football matches, or managing their allowance for gadgets, mastering numbers boosts confidence for everyday life. Our interactive lessons make learning both fun and simple. Since kids in Bahrain learn differently, we tailor our approach to fit every learner. From Manama’s lively city to peaceful beaches, BrightChamps brings math to life, making the LCM a fun part of every child’s math journey!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

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