# What is the Least Common Multiple of 6 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 6 and 12 is **12**.

LCM(6,12) = 12

## Least Common Multiple of 6 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 6 and 12, than apply into the LCM equation.

GCF(6,12) = 6

LCM(6,12) = ( 6 × 12) / 6

LCM(6,12) = 72 / 6

LCM(6,12) = 12

## Least Common Multiple (LCM) of 6 and 12 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 12. First we will calculate the **prime factors of 6 and 12**.

### Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of **6** in exponential form is:

6 = 2^{1} × 3^{1}

### 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 6 and 12**.

LCM(6,12) = 2^{2} × 3^{1}

LCM(6,12) = 12

## Recent Comments

so do i have to multiply only when there is lcm involved? do i have to multiply when there is gcm or no?

Give a formula that a standard 4 pupil can understand.

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