174 LearnersLast updated on May 26th, 2025
LCM of 12 and 15
LCM is a common multiple, the smallest value between the numbers 12 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 12 and 15?
The LCM of 12 and 15 is 60. 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 12 and 15 Using Listing the Multiples
Step1; Write down the multiples of the numbers. Don’t stop too early.
12 = 12,24,48,60 …
15 = 15,60,45,60,75,…
Step 2: Find the smallest number common between the written multiples of 12 and 15
— The smallest common multiple is 60.
Thus, LCM(12,15) = 60
LCM of 12 and 15 Using Prime Factorization
Step 1— factorize the numbers into its prime factors
12 =2×2×3
15 =5×3
Step 2— find the highest powers of the factors of 12 and 15
Step 3— Multiply the highest powers
LCM(12,15) = 60
LCM of 12 and 15 Using Division Method
- Write the numbers 12, 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(12,15) = 60
Common Mistakes and how to avoid them while finding the LCM of 12 and 15
Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 12 and 15. Try to avoid them.
Mistake 1
Listing incorrect multiples
If the LCM of given numbers is 60, double-check that the number appears on the list of both 12 and 15.
LCM of 12 and 15 Examples
Problem 1
The GCF of two numbers is 3, and one of the numbers is 12. If the LCM of the two numbers is 60, find the missing number.
Using the formula LCM(a,b)×GCF(a,b)=a×b:
60×3=12×Missing Number
180=12×Missing Number
Missing Number=180/12=15
Explanation
The missing number is 15.
Problem 2
Find the ratio of the GCF to the LCM of 12 and 15.
GCF of 12 and 15 = 3 (from Problem 3)
LCM of 12 and 15 = 60 (from Problem 1)
Ratio = GCF/LCM=3/60=1/20
Explanation
The ratio of the GCD to the LCM is 1:20.
Problem 3
Add the fractions 5/12 and 7/15 by finding the LCM of the denominators.
Answer: 5/12+7/15=53/60
Explanation
LCM of 12 and 15 = 60
Convert to common denominator:
5/12=5×5/60=25/60
7/15=7×4/60=28/60​
Sum: 25/60+28/60=53/60
FAQs on LCM of 12 and 15
1.What is the LCM of 5,15 and 20?
2.What is the HCF of 5 and 20?
3. Is 20 a multiple of 5?
4. Is 0 a multiple of 5?
5.What is the LCM of 17 and 11?
Important glossaries on the LCM of 12 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
: She loves to read number jokes and games.
