Least Common Multiple of 12 and 16

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 12 and 16 the smallest integer that is 48 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 16 is 48.

LCM(12,16) = 48

LCM of 12 and 16

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 12 and 16

LCM of 12 and 16 is 48

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


2 12
2 6
3 3
1

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

12 = 22×31

Prime Factorization of 16


2 16
2 8
2 4
2 2
1

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

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1, 2, 4, 8, 16

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

Properties of LCM 12 and 16

(i) The LCM of 16 and 12 is associative

LCM of 12 and 16 = LCM of 16 and 12

Related Least Common Multiples of 12

Related Least Common Multiples of 16

Frequently Asked Questions on LCM of 12 and 16

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.