276 LearnersLast updated on 5 August 2025
Finding the LCM of 3 and 6
When we synchronize events, make music or even when we set alarms, we use the LCM. In this article, we will discuss the LCM of 3 and 6.
How to find the LCM of 3 and 6?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 3 and 6 Using Listing the Multiples
use the following steps to find the LCM
Step 1: Write down the multiples of each number
— Multiples of 3 = 3,6,9,12,18 …
— Multiples of 6 = 6, 12,18,24,…
Step 2: Ascertain the smallest multiple from the listed multiples
— The smallest common multiple is 6.
Thus, LCM(3, 6) = 6.
LCM of 3 and 6 Using Prime Factorization
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Step1: Write the prime factors of the numbers:
— Prime factorization of
3 = 3
6 = 2×3
Step2: Pick the highest powers of each prime factor:
— Highest power of 3 = 3
— Highest power of 6 = 2
Step3: highest powers are to be multiplied to get the LCM:
LCM(3, 6) = 3 × 2= 6
LCM of 3 and 6 using the Division Method
Step 1: Write the numbers in a row
Step 2: Divide by common prime factors and multiply the divisors:
— 3 × 2 = 6
Thus, LCM(3, 6) = 6.
Common Mistakes and how to avoid them in LCM of 3 and 6
Listed below are a few commonly made mistakes when we try to find the LCM of 3 and 6
Mistake 1
Confusing LCM for HCF
The HCF of 3 and 6 is 3, and the LCM is 6.
LCM deals with multiples of the numbers 3 and 6. HCF focuses on divisors.
Mistake 2
Skipping the prime factors of the given numbers.
writing the prime factorization of 6 as 2×2 instead of 2×3. Such incorrect prime factorization will give you incorrect LCM.
Mistake 3
Multiplying the numbers directly:
The LCM of 3 and 6 is 6 and not 18, which is the product. One cannot make the assumption that the product is the LCM in cases where the numbers are not co-prime.
LCM of 3 and 6 Examples
Problem 1
Helicopter A and Helicopter B take trips every 3 hours and 6 hours to distribute food at the same time. In how long will they land together?
The LCM of 3 and 6 = 6
Explanation
The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the helicopters in 6 hours. LCM expresses the smallest common time interval between the given digits.
Problem 2
LCM of (3,x) is 6. Find x.
The LCM of x and 3 is 6, which means that the possible value of x is a divisor of 6. The divisors of 6 are 1,2,3,6.
Now we check for each of the factors;
LCM (3,1) = 3
LCM (3,2) =6
LCM (3,3) = 3
LCM (3,6) = 6
Explanation
The value of x can be either 2 or 6 as the LCM of 6 can be obtained using both.
Problem 3
Is 30 a common multiple of 3 and 6. Verify.
To check if 30 is a common multiple of 3 and 6, we check the divisibility of the numbers;
30/3 = 10
30/6 = 5
Explanation
30 is a common multiple of both 3 and 6 as there are no remainders left behind on division.
FAQs on 3 and 6
1.What is the LCM of 3,6 and 2?
2.What is the LCM of 3 and 6?
3.What are the factors of 3 and 6?
4.What is the smallest factor of 3 and 6 ?
5. Is 3 a prime factor of 6?
6.How can children in India use numbers in everyday life to understand Finding the LCM of 3 and 6?
7.What are some fun ways kids in India can practice Finding the LCM of 3 and 6 with numbers?
8.What role do numbers and Finding the LCM of 3 and 6 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Finding the LCM of 3 and 6 skills?
Important glossaries for the LCM of 3 and 6
- Multiple — It is a product of a number and any natural integer. So for 6, 6,12,18,..etc are the multiples.
- Prime Factor — It is a prime number that one gets after factorization of any given number. Like for 6 - 2,3, and 6 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.
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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.
