Least Common Multiple of 9 and 21

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

• Least Common Multiple of 9 and 21 by Prime method
• Least Common Multiple of 9 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 21. First we will calculate the prime factors of 9 and 21.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 21

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 3¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 21.

LCM(9,21) = 3²×7¹
LCM(9,21) = 63

Factors of 9

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

1, 3, 9

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 21, than apply into the LCM equation.

GCF(9,21) = 3
LCM(9,21) = ( 9 × 21) / 3
LCM(9,21) = 189 / 3
LCM(9,21) = 63

(i) The LCM of 21 and 9 is associative

LCM of 9 and 21 = LCM of 21 and 9

1. What is the LCM of 9 and 21?

Answer: LCM of 9 and 21 is 63.

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 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 9 and 21?

Answer:

Least Common Multiple of 9 and 21 = 63

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 21

21 = 3 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 = 63 = 3 x 3 x 7

Step 4: Therefore, the least common multiple of 9 and 21 is 63.