# What is the Least Common Multiple of 9 and 12?

*Least common multiple* or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 9 and 12 is **36**.

LCM(9,12) = 36

## 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 (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

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

9 = 3^{2}

### Prime Factorization of 12

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

12 = 2^{2} × 3^{1}

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

LCM(9,12) = 3^{2} × 2^{2}

LCM(9,12) = 36

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