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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 9 and 12 with Primes

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

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 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

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

LCM(9,12) = 22×32
LCM(9,12) = 36

Factors of 9

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

1, 3, 9

Factors of 12

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

1, 2, 3, 4, 6, 12

Least Common Multiple of 9 and 12 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 12, than apply into the LCM equation.

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

Least Common Multiple of 9 and 12 by Listing Multiples

Multiples of 9

9, 18, 27,36

Multiples of 12

12, 24,36

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 9 and 12 is 36

Properties of LCM 9 and 12

(i) The LCM of 12 and 9 is associative

LCM of 9 and 12 = LCM of 12 and 9

Frequently Asked Questions on LCM of 9 and 12

1. What is the LCM of 9 and 12?

Answer: LCM of 9 and 12 is 36.

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 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.

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

Answer:

Least Common Multiple of 9 and 12 = 36

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 12

12 = 2 x 2 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 9 and 12 is 36.