156 LearnersLast updated on May 26th, 2025
LCM of 2,3 and 7
The LCM comes in use when we need to find a shared pattern between numbers that seem unrelated. We apply LCM to synchronize cycles or schedules, syncing digital signals and finding compatible frequencies in technology. In this article, we’ll take a look at the LCM of 2,3 and 7.
What is the LCM of 2,3 and 7?
The LCM of 2,3 and 7 is the smallest positive integer that is a multiple of all the numbers. We find the LCM using the listing multiples method, the prime factorization method and the long division method.
LCM of 2,3 and 7 using the Listing Multiples Method
The LCM of 2,3 and 7 can be found using the following steps:
Step 1: Write the multiples of each number
Multiples of 2 = 2,4,6,8,10,12,14,…42,…
Multiples of 3 = 3,6,9,12,18,…42
Multiples of 7 = 7,14,21,28,35,42,…
LCM(2,3,7) = 42
Step 2: Find the smallest multiple from the listed multiples
The smallest common multiple is 42.
Thus, LCM (2,3,7) = 42
LCM of 2,3 and 7 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 the numbers.
Prime factorization of 3 = 31
Prime factorization of 2 = 21
Prime factorization of 7 = 71
Step 2:Take the highest powers of each prime factor. Multiply the highest powers to get the LCM
LCM(2,3,7) = 42
LCM of 2,3 and 7 using the Division Method
- Write the numbers 2,3 and 7 in a row
- Divide them by their common prime factors, if there is one
- Carry forward the numbers that are left undivided by the previously chosen factor
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM (2,3,7) = 42
Common Mistakes and how to avoid them while finding the LCM of 2,3 and 7
It is not unusual that kids make mistakes when trying to find the LCM of the numbers 4,5 and 7.
This may be due to unclear understanding of the concept or confusion. Make sure to avoid these!
Mistake 1
Confusing between LCM and HCF
LCM is the smallest number divisible by 2,3 and 7 while, the largest number that divides them both is the HCF.
LCM of 2,3 and 7, examples
Problem 1
LCM (2,6,7) = LCM(2,3,7) → Verify.
LCM of 2,6,7;
Prime factorization of 2 = 21
Prime factorization of 6 = 21×31
Prime factorization of 7 = 71
LCM(2,6,7) = 42
LCM of 2,3,7;
Prime factorization of 3 = 31
Prime factorization of 2 = 21
Prime factorization of 7 = 71
LCM(2,3,7) = 42
Explanation
LHS is equal to the RHS, the statement is true.
Problem 2
a=2, b=3, c=7. Verify using → LCM(a,b,c) = LCM(LCM(a,b),c)
LCM of 2,3;
Prime factorization of 3 = 31
Prime factorization of 2 = 21
LCM(2,3) = 6
Use the obtained LCM in the below;
LCM of 6,7;
Prime factorization of 6 = 21×31
Prime factorization of 7 = 71
LCM(6,7) = 42
Explanation
LCM(2,3,7) =42, it verifies with the given formula.
Problem 3
Find x, LCM(3,9,x) = 72
We know that the LCM of 3,9 = 9
The prime factorization of 72 = 23×32
The LCM of 3,9 already includes 32, and the factor of x must include 23, which is 8.
Explanation
By following the above assumption we assume that the value of x is 8.
FAQs on LCM of 2,3 and 7
1.What is the LCM of 2,4 and 7?
2. What is the GCF of 3, 9, and 12?
3.Find the LCM of 3 and 4.
4.What is the LCM of 9 and 12?
5. What is the LCM of 4,2 and 8?
6.How can children in United Kingdom use numbers in everyday life to understand LCM of 2,3 and 7?
7.What are some fun ways kids in United Kingdom can practice LCM of 2,3 and 7 with numbers?
8.What role do numbers and LCM of 2,3 and 7 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 2,3 and 7 skills?
Important glossaries for the LCM of 2,3 and 7
- Multiple — product of a number and a natural integer
- Prime factor — number one gets after prime factorization any given number
- Prime factorization — the process of breaking the number into its prime factors.
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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.
