# What is the Least Common Multiple of 123 and 135?

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 123 and 135 is 5535.

LCM(123,135) = 5535

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## Least Common Multiple of 123 and 135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 123 and 135, than apply into the LCM equation.

GCF(123,135) = 3
LCM(123,135) = ( 123 × 135) / 3
LCM(123,135) = 16605 / 3
LCM(123,135) = 5535

## Least Common Multiple (LCM) of 123 and 135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 123 and 135. First we will calculate the prime factors of 123 and 135.

### Prime Factorization of 123

Prime factors of 123 are 3, 41. Prime factorization of 123 in exponential form is:

123 = 31 × 411

### Prime Factorization of 135

Prime factors of 135 are 3, 5. Prime factorization of 135 in exponential form is:

135 = 33 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 123 and 135.

LCM(123,135) = 33 × 411 × 51
LCM(123,135) = 5535