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Last updated on May 26th, 2025

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LCM of 3 and 10

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The smallest number that should also be a positive number, and evenly divide both the numbers, is known as the least common factor. LCM is very important for solving problems, especially fractions, scheduling events etc.

LCM of 3 and 10 for UK Students
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What is the LCM of 3 and 10

The LCM of 3 and 10 is the lowest number that divides both 3 and 10 without leaving any remainder. The LCM of 3 and 10 is 30.

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How to find the LCM of 3 and 10?

The LCM of 3 and 10 can be found by the following methods like division method, listing multiples, prime factorization.
 

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LCM of 3 and 10 using Division method:

In the division method, we divide both the numbers by the lowest possible number until we get 1 for both numbers.

 

3 divides 3 leaving 1


2 divides 10 leaving 5


5 divides 5 leaving 1

 

LCM = 2 × 3  × 5= 30.
 

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LCM of 3 and 10 using Listing multiples:

We write the multiples of both numbers till we find the common one.


Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30…


Multiples of 10: 10, 20, 30…

 

The common multiple is 30. So, the LCM of 3 and 10 is 30.
 

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LCM of 3 and 10 using prime factorization:

We part each number into divisors and select the highest powers of all the prime factors.

 

3=  3


10= 2 × 5

 

LCM = 2 × 3 × 5= 30.
 

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Common Mistakes and How to Avoid Them in LCM of 3 and 10

While solving problems on LCM, children are likely to make common mistakes, here are a few mistakes and how to avoid them

Mistake 1

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 Not including the prime factors with the right ones.
 

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Children sometimes get confused and do not include the prime factors, instead of writing 9=3×3 they write 9=3×1. Students should always break numbers into prime numbers.
 

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Examples of LCM of 3 and 10

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Problem 1

Find the LCM of 3 and 10.

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Thus, the LCM of 3 and 10is 30.
 

Explanation

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30…


Multiples of 10: 10, 20, 30…


The common multiple is 30. So, the LCM of 3 and 10 is 30.

 

Thus, the LCM of 3 and 10is 30.
 

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Problem 2

Solve the following expression using LCM of 3 and 10: 1/3 + 1/10

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The sum of  1/3 and 1/10 is 13/30

Explanation

LCM(9,10)=90

 

1/3 = 10/30 , 1/10=3/30

 

Add the fractions:


10/30 + 3/30 = 13/30


The sum of  13 and 110 is 1330.
 

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Problem 3

Simplify the expression: x/3 + x/10 = 13

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The LCM of 3 and 10 is 30 based on their prime factors 2,3, and 5.
 

Explanation

 LCM (3,10) =30

 

10x/30 + 3x/30 =13

 

10x+3x/30=13 


13x= 13 × 30


13x = 390


x=30.


The LCM of 3 and 10 is 30 based on their prime factors 2,3, and 5.
 

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FAQ’s on LCM of 3 and 10

1.What is the GCF of 48,36,96?

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2.Is 0 a perfect number?

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3.What is the GCF of 10 and 3?

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4.Is 720 a multiple of 360?

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5.What is the GCF of 12 and 18?

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6.How can children in United Kingdom use numbers in everyday life to understand LCM of 3 and 10?

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7.What are some fun ways kids in United Kingdom can practice LCM of 3 and 10 with numbers?

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8.What role do numbers and LCM of 3 and 10 play in helping children in United Kingdom develop problem-solving skills?

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9.How can families in United Kingdom create number-rich environments to improve LCM of 3 and 10 skills?

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Important glossaries for LCM of 3 and 10

  • Co-prime: two numbers that have only one number that is 1 as their common factor.  For example, 8 and 15 are co-prime numbers.

 

  • Even Number: A natural number is divisible by 2. For example, 2,4,68,10 etc.

 

  • Prime Factorization: The process of parting down a number into its prime factors is called Prime Factorization.  For example, prime factorization of 24 = 2 × 2 × 2 × 3.
     
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About BrightChamps in United Kingdom

At BrightChamps, we know numbers are far more than mere digits—they open doors to endless opportunities! We aim to support children all over the United Kingdom in mastering essential math skills, with today’s spotlight on the LCM of 3 and 10 and a special focus on understanding the LCM—in a lively, enjoyable, and easy-to-understand way. Whether your child is working out how fast a roller coaster travels at Alton Towers, tracking scores at a local football match, or budgeting pocket money for the latest gadgets, mastering numbers helps build their everyday confidence. Our interactive lessons make learning fun and straightforward. Since children in the UK learn in diverse ways, we adapt our teaching to suit each individual. From the bustling streets of London to the scenic coastlines of Cornwall, BrightChamps makes math relatable and exciting throughout the UK. Let’s bring the LCM to life for 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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Fun Fact

: She loves to read number jokes and games.

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