164 LearnersLast updated on May 26th, 2025
LCM of 12 and 16
LCM is a common multiple, the smallest value between the numbers 3 and 8. 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 16?
The LCM of 3 and 8 is 24. 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 16 Using Listing the Multiples
Write down the multiples of the numbers. Don’t stop too early.
Step 1 — Multiples of 12 = 12, 24, 36, 48, 60, 72,84,96, …
Step 2 — Multiples of 16 = 16, 32, 48,64,80,96,…
Find the smallest number common between the written multiples of 12 and 16
Step 3— The smallest common multiple is 48
Thus, LCM(12,16) = 48
LCM of 12 and 16 Using Prime Factorization
Step 1 — factorize the numbers into its prime factors
12 = 2×2×3
16 = 2 × 2 ×2 × 2 ×2
Step 2 — find the highest powers of the factors of 12 and 16
Step 3 — Multiply the highest powers
LCM (12,16) = 48
LCM of 12 and 16 Using Division Method
- Write the numbers 12,16 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(12,16) = 48
Common Mistakes and how to avoid them while finding the LCM of 12 and 16
Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 12 and 16. Try to avoid them.
Mistake 1
Listing incorrect multiples
If the LCM of given numbers is 48, double-check that the number appears on the list of both 12 and 16
LCM of 12 and 16 examples
Problem 1
If 25% of the LCM of 12 and 16 is used to distribute supplies, how many supplies are distributed?
LCM of 12 and 16 = 48
25% of 48 = 0.25 × 48 = 12 supplies
Explanation
Multiply the LCM by 0.25 to find 25%.
Problem 2
A maintenance schedule for projectors is set up every 12 weeks and 16 weeks at a school. If both the projectors are serviced today, in how many weeks will they be serviced again on the same day?
The LCM of 12 and 16 is 48.
Explanation
Both projectors will need maintenance again in 48 weeks.48 is the LCM of 12 and 16, which is the smallest time interval between the digits.
Problem 3
Verify the formula LCM(a,b)=a×b/GCF(a,b) ​for 12 and 16.
GCF of 12 and 16 = 4
Product of 12 and 16 = 12 × 16 = 192
Using the formula:
LCM=192/4=48
Explanation
Apply the formula and check that the result matches the LCM.
The LCM (6,8,12) = 24
FAQs on LCM of 12 and 16
1.What is the LCM of 6,12 and 16?
2.What are the factors of 12 and 16 ?
3.What is the LCM of 6 and 16?
4.What is the HCF of 12 and 16?
5.What is the LCM of 6,8 and 12?
6.How can children in India use numbers in everyday life to understand LCM of 12 and 16?
7.What are some fun ways kids in India can practice LCM of 12 and 16 with numbers?
8.What role do numbers and LCM of 12 and 16 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 12 and 16 skills?
Important glossaries for the LCM of 12 and 16
- 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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