# Least Common Multiple of 9 and 14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9 and 14 the smallest integer that is 126 that is divisible by both numbers.

Least Common Multiple (LCM) of 9 and 14 is 126.

LCM(9,14) = 126

## LCM of 9 and 14

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

LCM of:
and ### LCM of 9 and 14 is 126

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 14. First we will calculate the prime factors of 9 and 14.

Prime Factorization of 9

 3 9 3 3 1

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 32

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

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 14.

LCM(9,14) = 21×32×71
LCM(9,14) = 126

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

Factors of 14

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

1, 2, 7, 14

### Least Common Multiple of 9 and 14 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 14, than apply into the LCM equation.

GCF(9,14) = 1
LCM(9,14) = ( 9 × 14) / 1
LCM(9,14) = 126 / 1
LCM(9,14) = 126

### Properties of LCM 9 and 14

(i) The LCM of 14 and 9 is associative

LCM of 9 and 14 = LCM of 14 and 9

### Frequently Asked Questions on LCM of 9 and 14

1. What is the LCM of 9 and 14?

Answer: LCM of 9 and 14 is 126.

2. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

3. 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.

4. How to Find the LCM of 9 and 14?

Least Common Multiple of 9 and 14 = 126

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 14

14 = 2 x 7

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

LCM = 126 = 2 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 9 and 14 is 126.