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.
 

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.
 

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.
 

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

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.
 

• 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.