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150 LearnersLast updated on November 29th, 2024
LCM of 3, 5 and 10
LCM is the smallest number divisible by 3, 5 and 10. LCM helps to solve problems with fractions, and scenarios like managing supplies and restocking. In this article, we will learn how to find LCM of 3, 5 and 10 by using different methods.
What is the LCM of 3, 5 and 10?
The LCM of 3, 5 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
How to find the LCM of 3, 5 and 10?
There are various methods to find the LCM. The methods to find the LCM are:
- Listing method
- Prime factorization method
- Division method
LCM of 3, 5 and 10 using the Listing Method
In the listing method, we write a multiple of the numbers first and then find the smallest common multiple.
Step 1: Identify the multiples of 3, 5 and 10
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50….
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90….
Step 2: Ascertain the smallest multiple from the listed multiples of 3, 5 and 10
The LCM of 3, 5 and 10 is 30
LCM of 3, 5 and 10 using the Prime Factorization Method
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 3, 5 and 10
Prime factorization of 3: 31
Prime factorization of 5: 51
Prime factorization of 10: 21 × 51
Step 2: Multiply the highest power of each factor ascertained to get the LCM
LCM of 3, 5 and 10 = 21 × 31 × 51 = 30
LCM of 3, 5 and 10 using the Division Method
This method involves simultaneously dividing the numbers by their prime factors until they become 1 and multiplying the divisors to get the LCM.
Step 1: Write the numbers in a row, like 3, 5, 10.
Step 2: Start dividing the numbers with prime factors by 2
From the numbers 3, 5 and 10, only 10 is divisible by 2 (10 ÷
2) which gives 5 as the quotient.
Now the numbers in the row will be 3, 5, 5
Step 3: Move on to the next prime number, 3
From the list 3, 5 and 5, only 3 is divisible by 3 (3 ÷ 3) which gives 1 as the quotient.
Now the numbers in the row will look like 1, 5, 5.
Step 4: Move on to the next prime number 5.
From the list 1, 5 and 5, only 5 is divisible by 5 (5 ÷ 5) which gives 1 as the quotient.
Now the numbers in the row will look like 1, 1, 1.
Step 5: To find the LCM, multiply all the divisors used
The divisors used are 2, 3 and 5. The product of 2, 3 and 5 is 30 (2×3×5 = 30)
Common Mistakes and how to avoid them while finding the LCM of 3, 5 and 10
LCM of 3, 5 and 10, Examples
Problem 1
Can you tell whether the LCM of 3, 5 and 10 is 30? Also find the GCF of 3, 5 and 10
Explanation
Problem 2
Runner A runs every 3 minutes in a trail and runner B every 5 minutes and runner C runs every 10 minutes, and both of them start together. When will they both meet at the starting point again?
Explanation
Problem 3
What will be the product when the LCM of 3,5 and 10 is multiplied twice?
Explanation
FAQs on LCM of 3, 5 and 10
1.What is the LCM of 3 5 10 15?
2.What is the LCM of 3, 4 and 10?
3.Is the LCM of 3 and 5 15?
4.What is the LCM of 3, 5 and 9?
5. What is the LCM of 12 and 24?
Important Glossaries for LCM of 3,5 and 10
- 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.
- LCM: The least common multiple is the smallest number divisible by two or more numbers.
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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.
