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124 LearnersLast updated on December 30th, 2024
LCM of 3, 6, and 7
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 3, 6 and 7. By learning the following tricks, you can learn the LCM of 3, 6, and 7 easily.
What Is the LCM of 3, 6, and 7?
The LCM of 3, 6, and 7 is 42. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.
How to find the LCM of 3, 6, and 7?
We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:
Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method
Now let us delve further into these three methods and how it benefits us.
LCM of 3, 6, and 7 Using Listing of Multiples Method
In this method, we will list all the multiples of 3, 6 and 7. Then we will try to find a multiple that is present in all three numbers.
For example,
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45…
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, ….
Multiples of 7
7, 14, 21, 28, 35, 42, 49, 56, …
The LCM of 3, 6, and 7 is 42. 42 is the smallest number which can be divisible by both 3, 6 and 7.
LCM of 3, 6, and 7 Using Prime Factorization
To find the LCM of 3, 6, and 7 using the prime factorization method, we need to find out the prime factors of both the numbers. Then multiply the highest powers of the factors to get the LCM.
Prime Factors of 3 are: 31
Prime Factors of 6 are: 21 and 31.
Prime Factors of 7 are: 71
Multiply the highest power of both the factors: 21 × 31 × 71 = 2 × 3 × 7 = 42
Therefore, the LCM of 3, 6, and 7 is 42
LCM of 3, 6, and 7 Using Division Method
To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.
For finding the LCM of 3, 6, and 7 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 3, 6, and 7.
2 × 3 × 7 = 42
The LCM of 3, 6, and 7 is 42
Common Mistakes and How to Avoid Them in LCM of 3, 6, and 7.
LCM of 3, 6, and 7 Examples
Problem 1
The LCM of 3, x, 7 is 42. Find the value of x
Explanation
Problem 2
Three bells ring in 3, 6, and 7 minutes of interval. At what time will they start ringing together if they start ringing at 2 in the morning?
Explanation
Problem 3
What will be the sum of LCM and GCF of 3, 6, and 7?
Explanation
FAQs on LCM of 3, 6, and 7
1.What are the multiples of 3,6 and 7?
2.What is the LCM of prime numbers?
3.What will be the LCM of identical numbers?
4.What is the GCF of 5 and 10?
5.What is the LCM of 4 and 8?
Important Glossaries for the LCM of 3, 6, and 7
- Prime Number: Any number that has only 2 factors is called a prime number.For 5 and 7, only common factors are 1 and the number itself.
- Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4,8 and 10.
- Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
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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.
