What is the lcm of 16 and 12

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 12 and 16.

Follow the steps below, and let's calculate the LCM of 12 and 16.

Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 12 and 16:

The prime factors of 12 are 2, 2 and 3. Prime factorization of 12 in exponential form is:

12 = 22x31

The prime factors of 16 are 2, 2, 2 and 2. Prime factorization of 16 in exponential form is:

16 = 24

Step 2: Identify the highest power of each prime number from the above boxes:

Step 3: Multiply these values together:

Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 12 and 16.

The Least Common Multiple of 12 and 16 is 48.

Method 2 - List of Multiples

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 12:

12, 24, 36, 48, 60, 72, 84

Multiples of 16:

Therefore,

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 12 and 16 is 48.

LCM(12,16) = 48

Least Common Multiple of 12 and 16 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 16, than apply into the LCM equation.

GCF(12,16) = 4 LCM(12,16) = ( 12 × 16) / 4 LCM(12,16) = 192 / 4

LCM(12,16) = 48

Least Common Multiple (LCM) of 12 and 16 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 16. First we will calculate the prime factors of 12 and 16.

Prime Factorization of 12

Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:

12 = 22 × 31

Prime Factorization of 16

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 24

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 16.

LCM(12,16) = 24 × 31
LCM(12,16) = 48

1. What is the LCM of 12 and 16?

Answer: LCM of 12 and 16 is 48.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

4. How to Find the LCM of 12 and 16?

Answer:

Least Common Multiple of 12 and 16 = 48

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 48 = 2 x 2 x 2 x 2 x 3

Step 4: Therefore, the least common multiple of 12 and 16 is 48.

The LCM of 12 and 16 is 48.

Steps to find LCM

1. Find the prime factorization of 12
   12 = 2 × 2 × 3
2. Find the prime factorization of 16
   16 = 2 × 2 × 2 × 2
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

   LCM = 2 × 2 × 2 × 2 × 3

4. LCM = 48

MathStep (Works offline)

Find least common multiple (LCM) of: 24 & 32 6 & 8 36 & 48 60 & 80 84 & 112 24 & 16 12 & 32 36 & 16 12 & 48 60 & 16 12 & 80 84 & 16 12 & 112

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

LCM of 12 and 16 is the smallest number among all common multiples of 12 and 16. The first few multiples of 12 and 16 are (12, 24, 36, 48, 60, 72, . . . ) and (16, 32, 48, 64, 80, 96, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 16 - by prime factorization, by listing multiples, and by division method.

What is the LCM of 12 and 16?

Answer: LCM of 12 and 16 is 48.

Explanation:

The LCM of two non-zero integers, x(12) and y(16), is the smallest positive integer m(48) that is divisible by both x(12) and y(16) without any remainder.

Methods to Find LCM of 12 and 16

Let's look at the different methods for finding the LCM of 12 and 16.

• By Listing Multiples
• By Division Method
• By Prime Factorization Method

LCM of 12 and 16 by Listing Multiples

To calculate the LCM of 12 and 16 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and 16 (16, 32, 48, 64, 80, 96, 112, . . . . )
• Step 2: The common multiples from the multiples of 12 and 16 are 48, 96, . . .
• Step 3: The smallest common multiple of 12 and 16 is 48.

∴ The least common multiple of 12 and 16 = 48.

LCM of 12 and 16 by Division Method

To calculate the LCM of 12 and 16 by the division method, we will divide the numbers(12, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 16.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 16. Write this prime number(2) on the left of the given numbers(12 and 16), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 16) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
• Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 12 and 16 is the product of all prime numbers on the left, i.e. LCM(12, 16) by division method = 2 × 2 × 2 × 2 × 3 = 48.

LCM of 12 and 16 by Prime Factorization

Prime factorization of 12 and 16 is (2 × 2 × 3) = 22 × 31 and (2 × 2 × 2 × 2) = 24 respectively. LCM of 12 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 31 = 48.
Hence, the LCM of 12 and 16 by prime factorization is 48.

☛ Also Check:

LCM of 12 and 16 Examples

1. Example 1: Verify the relationship between GCF and LCM of 12 and 16.

   Solution:

   The relation between GCF and LCM of 12 and 16 is given as, LCM(12, 16) × GCF(12, 16) = Product of 12, 16

   Prime factorization of 12 and 16 is given as, 12 = (2 × 2 × 3) = 22 × 31 and 16 = (2 × 2 × 2 × 2) = 24

   LCM(12, 16) = 48 GCF(12, 16) = 4 LHS = LCM(12, 16) × GCF(12, 16) = 48 × 4 = 192 RHS = Product of 12, 16 = 12 × 16 = 192 ⇒ LHS = RHS = 192

   Hence, verified.

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The LCM of 12 and 16 is 48. To find the LCM (least common multiple) of 12 and 16, we need to find the multiples of 12 and 16 (multiples of 12 = 12, 24, 36, 48; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible by 12 and 16, i.e., 48.

If the LCM of 16 and 12 is 48, Find its GCF.

LCM(16, 12) × GCF(16, 12) = 16 × 12 Since the LCM of 16 and 12 = 48 ⇒ 48 × GCF(16, 12) = 192

Therefore, the GCF = 192/48 = 4.

Which of the following is the LCM of 12 and 16? 35, 42, 48, 32

The value of LCM of 12, 16 is the smallest common multiple of 12 and 16. The number satisfying the given condition is 48.

How to Find the LCM of 12 and 16 by Prime Factorization?

To find the LCM of 12 and 16 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (16 = 2 × 2 × 2 × 2). LCM of 12 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 16.
⇒ LCM of 12, 16 = 24 × 31 = 48.

What is the Least Perfect Square Divisible by 12 and 16?

The least number divisible by 12 and 16 = LCM(12, 16)
LCM of 12 and 16 = 2 × 2 × 2 × 2 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 12 and 16 = LCM(12, 16) × 3 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.