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Least Common Multiple of 9 and 12

Free LCM Calculator determines the least common multiple (LCM) between 9 and 12 the smallest integer that is 36 that is divisible by both numbers.

Least Common Multiple (LCM) of 9 and 12 is 36.

LCM(9,12) = 36

LCM of 9 and 12

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

LCM of:
and

Least Common Multiple (LCM) of 12 and 9 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 9. First we will calculate the prime factors of 12 and 9.

Prime Factorization of 12


2 12
2 6
3 3
1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

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

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 9.

LCM(12,9) = 22×32
LCM(12,9) = 36

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Factors of 9

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

1, 3, 9

Least Common Multiple of 12 and 9 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 9, than apply into the LCM equation.

GCF(12,9) = 3
LCM(12,9) = ( 12 × 9) / 3
LCM(12,9) = 108 / 3
LCM(12,9) = 36

Properties of LCM 12 and 9

(i) The LCM of 9 and 12 is associative

LCM of 12 and 9 = LCM of 9 and 12

Frequently Asked Questions on LCM of 12 and 9

1. What is the LCM of 12 and 9?

Answer: LCM of 12 and 9 is 36.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. 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.

4. How to Find the LCM of 12 and 9?

Answer:

Least Common Multiple of 12 and 9 = 36

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 9

9 = 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 = 36 = 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 12 and 9 is 36.