149 LearnersLast updated on May 26th, 2025
LCM of 3 and 10
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.
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.
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.
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.
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.
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.
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
Not including the prime factors with the right ones.
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.
Examples of LCM of 3 and 10
Problem 1
Find the LCM of 3 and 10.
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.
Problem 2
Solve the following expression using LCM of 3 and 10: 1/3 + 1/10
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.
Problem 3
Simplify the expression: x/3 + x/10 = 13
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.
FAQ’s on LCM of 3 and 10
1.What is the GCF of 48,36,96?
2.Is 0 a perfect number?
3.What is the GCF of 10 and 3?
4.Is 720 a multiple of 360?
5.What is the GCF of 12 and 18?
6.How can children in United States use numbers in everyday life to understand LCM of 3 and 10?
7.What are some fun ways kids in United States can practice LCM of 3 and 10 with numbers?
8.What role do numbers and LCM of 3 and 10 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 3 and 10 skills?
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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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
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