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365 LearnersLast updated on August 5, 2025
LCM of 5 and 12
LCM is a common multiple, the smallest value between the numbers 5 and 12. 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 5 and 12?
The LCM of 5 and 12 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 5 and 12 using the Listing Multiples Method
Step 1: Write down the multiples of the numbers. Don’t stop too early.
— Multiples of 5 = 5,10,15,20,26,30,35,40,45,50,55,60,…
— Multiples of 12 = 12, 24, 36, 48, 60, 52, 60, …
Step 2: Find the smallest number common between the written multiples of 3 and 8
— The smallest common multiple is 60
Thus, LCM(5,12) = 60
LCM of 5 and 12 using the Division Method
- Write the numbers 5,12 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(5,12) = 60
Common Mistakes and how to avoid them while finding the LCM of 5 and 12
Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 5 and 12. 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 5 and 12.
Mistake 2
Prime factorization errors
Check if the numbers are prime factored correctly. For example, we may accidentally write 12 = 2×2×2 instead of 12= 2×2×3
Mistake 3
Thinking product is the LCM
One may think the product of the numbers is the LCM of the numbers. This is only true in case of co-prime numbers.
LCM of 5 and 12, examples
Problem 1
A movie theater alternates between a crime film and a children’s film. The crime film is shown every 5 days and the children’s film is shown every 12 days. In how many days will they both be screened together?
The LCM of 5 and 12 is 60.
Explanation
Both films will be shown on the same day again in 60 days. The LCM of 5 and 12 is 60, which is the smallest common time interval between the digits.
Problem 2
How many times does the LCM of 5 and 12 occur between 1 and 300?
LCM of 5 and 12 is 60.
Divide 300 by 60 to find how many times it occurs: 300/60=5
Explanation
So, the LCM of 5 and 12 occurs 5 times between 1 and 300
Problem 3
Verify the LCM of 5 and 12 using the formula LCM(a,b)=aĂ—bGCD(a,b)
a=5, b=12
GCD of 5 and 12 is 1 (because 5 and 12 share no common factors).
Using the formula:
LCM(5,12)=5×12/1=60
Explanation
Therefore, the LCM is 60, confirming the result.
FAQs on LCM of 5 and 12
1.What is the LCM of 5,12 and 20?
2.What are the common factors of 5 and 12 ?
3.What are the multiples of 5 and 12?
4.What is the LCM of 5,4 and 12?
5.What is divisible by both 5 and 12?
Important glossaries for the LCM of 5 and 12
- 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.
