128 LearnersLast updated on May 26th, 2025
LCM of 2, 5, and 6
LCM of any two numbers is the least common multiple of two numbers. In our daily life, LCM is used for scheduling events, as distributing any items among others. In this topic, we will learn more about LCM of 2, 5, and 6.
What is the LCM of 2, 5, and 6
What is the LCM of 2, 5, and 6
How to find the LCM of 2, 5, and 6?
Out of many methods, prime factorization method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows -
- Listing Of Multiples
- Prime Factorization
- Division Method
LCM of 2, 5, and 6 Using Listing the Multiples
Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 3 numbers is noted -
- Multiples of 2:2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
- Multiples of 5:5, 10, 15, 20, 25, 30
- Multiples of 6:6, 12, 18, 24, 30
Then we can see that out of 2, 5, and 6, 30 is the smallest common number that is present in them. So we see that 30 is the LCM of 2, 5, and 6.
LCM of 2, 5, and 6 Using Prime Factorization
The product of the highest power of prime factors of 2, 5, and 6 is the LCM of these numbers. So let us look at it step by step to understand it better.
Breaking the given numbers into their prime factors.
- Prime factorization of 2 = 2
- Prime factorization of 5 = 5
- Prime factorization of 6 = 2 × 3
Multiplying the highest power of prime factors: 21 × 31 × 51 → 2 × 3 × 5 = 30
LCM of 2, 5, and 6 is 30.
The product of the highest power of prime factors of 2, 5, and 6 is the LCM of these numbers. So let us look at it step by step to understand it better.
Breaking the given numbers into their prime factors.
Prime factorization of 2 = 2
Prime factorization of 5 = 5
Prime factorization of 6 = 2 × 3
Multiplying the highest power of prime factors: 21 × 31 × 51 → 2 × 3 × 5 = 30
LCM of 2, 5, and 6 is 30.
LCM of 2, 5, and 6 Using Division Method
In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.
- Step 1: Arrange the number in a sequence, divisors, and the numbers are on the left and right sides respectively.
- Step 2: For finding the divisor, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 2, 5, and 6 by 2. The result is 1, 5, and 3.
- Step 3: As 3 is divisible by 3. Dividing 1, 5, and 3 by 3. Now the result is 1, 5, and 1.
- Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.
The divisors are 2, 3, 5. LCM of 2, 5, and 6 is the product of divisors.
Hence, the LCM of (2, 5, and 6) = 2 × 3 × 5 = 30
Common Mistakes and How to Avoid Them in LCM of 2, 5, and 6
There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.
Mistake 1
Confusing factors and multiples.
Students used to confuse factors and multiples. To avoid confusion, students need to understand the concept of multiples and factors. Multiplies of a number are the product of the number with whole numbers, whereas factors of the number are the numbers which can evenly divide the number. For example, 1, 2, 3, 4, 6, and 12 are the factors of 12; whereas 12, 24, 36, 48, 60,… are the multiples of 12.
LCM of 2, 5, and 6 Examples
Problem 1
A bus arrives every 2 minutes and another bus arrives every 6 minutes, if both buses arrive at 7: 00 AM. when will they arrive together again?
First find the LCM of 2 and 5 :
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
Multiples of 5: 5, 10, 15, 20, 25, 30
Here, the smallest common multiple of 2 and 6 is 6.
Explanation
The buses will arrive together again after 6 minutes, if the buses arrive at 7:00 AM. then they will arrive together at 7: 06 AM.
Problem 2
A teacher wants to schedule two classes. One repeats every 2 days, and the other repeats every 5 days, if both classes meet on the same day, when will they meet on the same day again?
Find the LCM of 2 and 5
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….
Multiples of 5: 5, 10, 15, 20, 25, 30
The smallest common multiple of 2 and 5 is 10.
Explanation
To find the LCM, write the multiples and select the smallest common multiple. 10 is the LCM of 2 and 5. So the 10 means, the class will meet together again after 10 days.
Problem 3
A school bus comes every 2 minutes, and a community bus comes every 5 minutes, if both buses arrive at the station at 8:00 AM. When will they arrive together again?
Here, to calculate the LCM of 2 and 5
Write the multiple of 2 and 5 :
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….
Multiples of 5: 5, 10, 15, 20, 25, 30
The smallest common multiple of 2 and 5 is 10. 10 means 10 minutes.
Explanation
So both buses arrive together again at 8:10 AM.
FAQ on LCM of 2, 5 and 6
1.What are the multiples of 2, 5, and 6?
2.What is the LCM of 2, 6, and 6?
3.What is the LCM of 2, 5, and 6?
4.What is the LCM of 5 and 7?
5.What is the LCM of 9 and 12?
6.How can children in United Kingdom use numbers in everyday life to understand LCM of 2, 5, and 6?
7.What are some fun ways kids in United Kingdom can practice LCM of 2, 5, and 6 with numbers?
8.What role do numbers and LCM of 2, 5, and 6 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve LCM of 2, 5, and 6 skills?
Important Glossaries of LCM 2, 5, and 6
- Factor: A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.
- Prime Factorization: When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.
- Greatest Common Factor (GCF): GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.
- Division Method: In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 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.
