182 LearnersLast updated on May 26th, 2025
LCM of 2 and 6
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 and 6. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 2 and 6?
The LCM of 2 and 6 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.
How to find the LCM of 2 and 6 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 2 and 6 using the Listing multiples method
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Step 1: Writedown the multiples of each number:
Multiples of 2 = 2,4,6,8,10,12…
Multiples of 6 = 6,12,18…
Step 2: Ascertain the smallest multiple from the listed multiples of 2 and 6.
The LCM (The Least common multiple) of 2 and 6 is 6. i.e.,6 is divisible by 2 and 6 with no reminder.
LCM of 2 and 6 using the Prime Factorization
This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.
Step 1: Find the prime factors of the numbers:
Prime factorization of 2 = 2
Prime factorization of 6 = 2×3
Step 2: Take the highest power of each prime factor:
2,3
Step 3: Multiply the ascertained factors to get the LCM:
LCM (2,6) = 2×3 = 6
LCM of 2 and 6 using the Division Method
The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1: Write down the numbers in a row;
Step 2: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
Step 3: The LCM of the numbers is the product of the prime numbers in the first column, i.e.,
2×3= 6
LCM (2,6) = 6
Common Mistakes and how to avoid them in LCM of 2 and 6
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 6 make a note while practicing.
Mistake 1
Confusing between LCM and HCF of the numbers 2 and 6
It is common for one to be confused between the HCF (Highest common factor) and LCM (least common multiple). LCM is the smallest number divisible by 2 and 6 while, the largest number that divides them both is the HCF.
A simple trick to remember is that the HCF is going to be a relatively smaller number than the LCM, as it deals with divisors.
LCM of 2 and 6 Examples
Problem 1
Use LCM(a,b)=|a×b|/HCF(a,b) to find the LCM of 2 and 6.
Let us assume, a= 2 and b= 6.
Applying the formula;
LCM(a,b)=|a×b|/HCF(a,b)
HCF of 2,6:
Factors of 2 = 1,2
Factors of 6 = 1,2,3,6
HCF (2,6) = 2
LCM(2,6)=|2×6|/2
12/2 = 6
Explanation
The above is how we ascertain the LCM of the numbers using the formula
Problem 2
Add the fractions 1/2 and 1/6.
First, we find the LCM of the denominators;
Prime factorization of 2 = 2
Prime factorization of 6 = 2×3
LCM (2,6) = 6
Now, we equate the denominators;
1/2 ×3/3 = 3/6
The denominator of 1/6 is already the LCM, so we do not equate its denominator.
We proceed to add the fractions;
3/6 + 1/6 = 4/6 → can be simplified to 2/3.
Explanation
The above is how we use LCM to find the sum of fractions. The same process can be applied to other arithmetic operations.
Problem 3
LCM of a and b is 6 and the HCF of the same two numbers is 1. Find a and b.
Given;
LCM (a, b) = 6
HCF (a, b) = 1
a = 2, b =3
Explanation
For the LCM to be 6 and the HCF to be 1, the numbers have to be coprime, i.e., they have no common factors but 1.
LCM (3,2) = 6, HCF(2,3) =1
FAQ’s on the LCM of 2 and 6
1.Is multiplying 2 and 6 the correct way to find the LCM?
2.Why is the LCM of 2 and 6, not 6?
3.What is the LCM formula using the HCF?
4.Is the LCM of 2 and 6 always a multiple of their HCF?
5.What is the LCM of 2,4,6 and 8 ?
6.How can children in Qatar use numbers in everyday life to understand LCM of 2 and 6 ?
7.What are some fun ways kids in Qatar can practice LCM of 2 and 6 with numbers?
8.What role do numbers and LCM of 2 and 6 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 2 and 6 skills?
Important Glossaries for LCM of 2 and 6
- 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.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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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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