143 LearnersLast updated on May 26th, 2025
LCM of 12, 14, and 16
Least Common Multiple (LCM) is the smallest positive integer that is divisible by 12, 14, and 16. By learning the following tricks, you can learn the LCM of 12, 14, and 16 easily.
What Is the LCM of 12, 14, and 16?
The LCM of 12, 14, and 16 is 336. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.
How to find the LCM of 12, 14, and 16?
We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:
Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method
Now let us delve further into these three methods and how it benefits us.
LCM of 12, 14, and 16 Using Listing of Multiples Method
In this method, we will list all the multiples of 12, 14, and 16. Then we will try to find a multiple that is present in all numbers.
For example,
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336…
Multiples of 14:
14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336,....
Multiples of 16:
16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336.
The LCM of 12, 14, and 16 is 366. 366 is the smallest number which can be divisible by 12, 14, and 16.
LCM of 12, 14, and 16 Using Prime Factorization
To find the LCM of 12, 14, and 16 using the prime factorization method, we need to find out the prime factors of the numbers. Then multiply the highest powers of the factors to get the LCM.
Prime Factors of 12 are: 22 × 31.
Prime Factors of 14 are: 21 × 71.
Prime Factors of 16 are: 24
Multiply the highest power of the factors: 24 × 31 × 71 = 16 × 3 × 7 = 336
Therefore, the LCM of 12, 14, and 16 is 336
LCM of 12, 14, and 16 Using Division Method
To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.
For finding the LCM of 12, 14, and 16 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 12, 14, and 16.
2 × 2 × 2 × 2 × 3 × 7 = 168
The LCM of 12, 14, and 16 is 366.
Common Mistakes and How to Avoid Them in LCM of 12, 14, and 16
Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
Mistake 1
Missing a prime factor
Children sometimes may forget to write all the prime factors for a given number. So, at the start we have to write all the prime factors for the given numbers which won’t cause any problems later on.
LCM of 12, 14, and 16 Examples
Problem 1
If the LCM of 12, 14, y is 336. Find ‘y’
The value of y is 16
Explanation
‘y’ is a divisor of 336. Try different values for ‘y’ other than 12 and 14. Here, y = 16 because it is a divisor of 336. Hence, 336 is the LCM.
Problem 2
The radius of the circle is the LCM of 12, 14, and 16. Find the diameter of the circle.
The radius is 336, and the diameter is 672
Explanation
Here, 336 is the LCM. So, the radius of the circle is 336. To find the diameter → ‘d = 2r’. The diameter of the circle = 2r = 2 × 336 = 672
Problem 3
What is the difference between LCM and GCF of 12, 14, and 16?
The difference is 334
Explanation
The LCM is 336 and the GCF is 2. Subtract them to get the result. Therefore, the difference of LCM and GCF is 334 (336–2)
FAQs on LCM of 12, 14, and 16
1.What is the sum of LCM and GCF of 12, 14, and 16?
2.Can prime numbers have LCM?
3.What will be the LCM of 5 and 6
4.What is the LCM of 13, 15, and 17?
5.Is the LCM of 12, 14, and 16 a perfect cube?
6.How can children in Philippines use numbers in everyday life to understand LCM of 12, 14, and 16?
7.What are some fun ways kids in Philippines can practice LCM of 12, 14, and 16 with numbers?
8.What role do numbers and LCM of 12, 14, and 16 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve LCM of 12, 14, and 16 skills?
Important Glossaries for the LCM of 12, 14, and 16
- Prime Number: Any number that has only 2 factors is called a prime number.For 5 and 7, only common factors are 1 and the number itself.
- Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4, 8, and 10.
- Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
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About BrightChamps in Philippines
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.
