Least Common Multiple of 14 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 14 and 16 the smallest integer that is 112 that is divisible by both numbers.

Least Common Multiple (LCM) of 14 and 16 is 112.

LCM(14,16) = 112

LCM of 14 and 16

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

LCM of:
and

Least Common Multiple of 14 and 16

LCM of 14 and 16 is 112

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 16. First we will calculate the prime factors of 14 and 16.

Prime Factorization of 14


2 14
7 7
1

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 21×71

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 14 and 16.

LCM(14,16) = 24×71
LCM(14,16) = 112

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

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 14 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 14 and 16, than apply into the LCM equation.

GCF(14,16) = 2
LCM(14,16) = ( 14 × 16) / 2
LCM(14,16) = 224 / 2
LCM(14,16) = 112

Properties of LCM 14 and 16

(i) The LCM of 16 and 14 is associative

LCM of 14 and 16 = LCM of 16 and 14

Related Least Common Multiples of 14

Related Least Common Multiples of 16

Frequently Asked Questions on LCM of 14 and 16

1. What is the LCM of 14 and 16?

Answer: LCM of 14 and 16 is 112.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

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 14 and 16?

Answer:

Least Common Multiple of 14 and 16 = 112

Step 1: Find the prime factorization of 14

14 = 2 x 7

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 = 112 = 2 x 2 x 2 x 2 x 7

Step 4: Therefore, the least common multiple of 14 and 16 is 112.