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153 LearnersLast updated on November 29th, 2024
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
LCM of 2,3 and 7, examples
Problem 1
LCM (2,6,7) = LCM(2,3,7) → Verify.
Explanation
Problem 2
a=2, b=3, c=7. Verify using → LCM(a,b,c) = LCM(LCM(a,b),c)
Explanation
Problem 3
Find x, LCM(3,9,x) = 72
Explanation
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?
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.
