215 LearnersLast updated on May 26th, 2025
LCM of 3 and 7
LCM helps to solve arithmetic operations in problems with fractions and helps in scheduling or aligning cycle of events that occur frequently.
What is the LCM of 3 and 7?
The LCM of 3 and 7 is 21 which is the smallest positive integer, a multiple of both numbers.
How to find the LCM of 3 and 7 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 3 and 7 using the Listing Multiples method
The LCM of 3 and 7 can be found using the following steps;
Step 1:Write down the multiples of each number:
Multiples of 3 = 3,6,9,12,15,18,21,…
Multiples of 7 = 7,14,21,…
Step 2:find the smallest multiple from the listed multiples of 3 and 7.
LCM(3,7) = 21
21 is divisible by 3 and 7 leaving no reminders.
LCM of 3 and 7 using the Prime Factorization
The numbers are prime factorized and their highest powers are multiplied.
Step 1: Write the prime factors of the numbers:
Prime factorization of 3 = 3
Prime factorization of 7 = 7
Step 2: Pick the highest power of each prime factor:
3,7
Step 3: Multiply the factors to get the LCM:
LCM (3,13) = 3×7 = 21
LCM of 3 and 7 using the Division method
Here we divide the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1: Write the numbers in a row;
Step 2:Divide the row of numbers with a number that is evenly divisible into at least one of the given numbers, and continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers has not been divisible previously.
Step 3: The LCM of the numbers is the product of the divisors
3×7= 21
LCM (3,7) = 21
Common Mistakes and how to avoid in LCM of 3 and 7
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3 and 7, make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 3 and 7
always double-check the multiples and do not stop too early.
LCM of 3 and 7, Examples
Problem 1
LCM of 7 and x is 21. Find x.
Solution: 3
Explanation
The LCM of x and 7 is 21, 21 is the product of 3 and 7, therefore the missing number must be 3.
Problem 2
Use LCM(a,b) = a×b/HCF(a,b) to find the LCM of 3 and 7.
The HCF of 3 and 7 is 1, they share no common factors.
Applying the formula;
LCM(a,b) = a×b/HCF(a,b)
LCM(3,7) = 3×7/1
LCM = 21
Explanation
Using the above formula and the method we find the LCM of any two numbers
Problem 3
Runner A can complete a lap in 3 minutes, and Runner B can complete a lap in 7 minutes. When will runners A and B meet at again?
LCM of 3 and 7 is 21.
Explanation
Runners A and B will meet again after 21 minutes, which is the LCM of 3 and 7.
FAQs on LCM of 3 and 7
1.What are the multiples of 3 and 7?
2.What is the LCM of 3,7 and 13?
3.What is the HCF of 3 and 7?
4.What is the LCM of 3,5 and 7 ?
5.Are 3 and 7 prime numbers?
6.How can children in United States use numbers in everyday life to understand LCM of 3 and 7?
7.What are some fun ways kids in United States can practice LCM of 3 and 7 with numbers?
8.What role do numbers and LCM of 3 and 7 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 3 and 7 skills?
Important glossaries for LCM of 3 and 7
- 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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