164 LearnersLast updated on May 26th, 2025
LCM of 6 and 15
LCM is a common multiple, the smallest value between the numbers 6 and 15. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.
What is the LCM of 6 and 15?
The LCM of 6 and 15 is 30. We can find the LCM using the Listing multiples method, the prime factorization method and the long division method. These are explained below.
LCM of 6 abd 15 Using Listing the Multiples
Step 1: Write down the multiples of the numbers. Don’t stop too early.
Multiples of 6 = 6,12,18,24,30,36, …
Multiples of 15 = 15,30,45,60,75,…
Step 2: Find the smallest number common between the written multiples of 3 and 8
The smallest common multiple is 30
Thus, LCM(6,15) = 30
LCM of 6 and 15 Using Prime Factorization
Step 1:factorize the numbers into its prime factors
6 = 3×2
15 = 3×5
Step 2: find the highest powers of the factors of 6 and 15
Step 3: Multiply the highest powers
LCM (6,15) = 30
LCM of 6 and 15 Using Division Method
- Write the numbers 6,15 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(6,15) = 30
Common Mistakes and how to avoid them while finding the LCM of 6 and 15
Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 3 and 8. Try to avoid them.
Mistake 1
Listing incorrect multiples
If the LCM of given numbers is 30, double-check that the number appears on the list of both 6 and 15
LCM of 6 and 15 Examples
Problem 1
The LCM of 6 and a number x is 30. Find x.
Prime factorization of 6: 2×3
LCM of 6 and x is 30, so x must contain the prime factor of 5 to reach 30 (since 6×5=30).
x=5
Explanation
The missing number x is 5.
Problem 2
Use the relationship LCM(a,b)×GCF(a,b)=a×b to verify the LCM of 6 and 15.
GCF(6,15)= 3
LCM(6,15)=30
Now verify:
LCM(6,15)×GCD(6,15)=30×3=90
6×15=90
Explanation
The equation holds true. The LCM is correct.
Problem 3
Simplify the sum 1/6+1/15​ using the LCM of the denominators.
Find the LCM of 6 and 15: LCM = 30
Rewrite the fractions:
16=5/30,1/15=2/30
Sum: 5/30+2/30=7/30
Explanation
The simplified sum is 7/30
FAQs on LCM of 6 and 15
1.What is the HCF of 6 and 15?
2.What is the LCM of 6,15 and 12?
3.Find the prime factors of each number:
4.What is the highest multiple of 6 and 15?
5.What are the factors of 15?
6.How can children in India use numbers in everyday life to understand LCM of 6 and 15?
7.What are some fun ways kids in India can practice LCM of 6 and 15 with numbers?
8.What role do numbers and LCM of 6 and 15 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 6 and 15 skills?
Important glossaries on the LCM of 6 and 15
- 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
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