# What is the Least Common Multiple of 54 and 66?

*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 54 and 66 is **594**.

LCM(54,66) = 594

## Least Common Multiple of 54 and 66 with GCF Formula

The formula of **LCM** is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 54 and 66, than apply into the LCM equation.

GCF(54,66) = 6

LCM(54,66) = ( 54 × 66) / 6

LCM(54,66) = 3564 / 6

LCM(54,66) = 594

## Least Common Multiple (LCM) of 54 and 66 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 66. First we will calculate the **prime factors of 54 and 66**.

### Prime Factorization of 54

Prime factors of 54 are 2, 3. Prime factorization of **54** in exponential form is:

54 = 2^{1} × 3^{3}

### Prime Factorization of 66

Prime factors of 66 are 2, 3, 11. Prime factorization of **66** in exponential form is:

66 = 2^{1} × 3^{1} × 11^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 54 and 66**.

LCM(54,66) = 2^{1} × 3^{3} × 11^{1}

LCM(54,66) = 594