Least Common Multiple of 9 and 18

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

• Least Common Multiple of 9 and 18 by Prime method
• Least Common Multiple of 9 and 18 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 18. First we will calculate the prime factors of 9 and 18.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 18

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 2¹×3²

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 18.

LCM(9,18) = 2¹×3²
LCM(9,18) = 18

Factors of 9

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

1, 3, 9

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 18, than apply into the LCM equation.

GCF(9,18) = 9
LCM(9,18) = ( 9 × 18) / 9
LCM(9,18) = 162 / 9
LCM(9,18) = 18

(i) The LCM of 18 and 9 is associative

LCM of 9 and 18 = LCM of 18 and 9

1. What is the LCM of 9 and 18?

Answer: LCM of 9 and 18 is 18.

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 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

4. How to Find the LCM of 9 and 18?

Answer:

Least Common Multiple of 9 and 18 = 18

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 18

18 = 2 x 3 x 3

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

LCM = 18 = 2 x 3 x 3

Step 4: Therefore, the least common multiple of 9 and 18 is 18.