Least Common Multiple of 9 and 14

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

• Least Common Multiple of 9 and 14 by Prime method
• Least Common Multiple of 9 and 14 with GCF Formula

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

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

9 = 3²

Prime Factorization of 14

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

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

(i) The LCM of 14 and 9 is associative

LCM of 9 and 14 = LCM of 14 and 9

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?

Answer:

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.