# What is the Least Common Multiple of 129 and 138?

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 129 and 138 is 5934.

LCM(129,138) = 5934

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## Least Common Multiple of 129 and 138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 129 and 138, than apply into the LCM equation.

GCF(129,138) = 3
LCM(129,138) = ( 129 × 138) / 3
LCM(129,138) = 17802 / 3
LCM(129,138) = 5934

## Least Common Multiple (LCM) of 129 and 138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 129 and 138. First we will calculate the prime factors of 129 and 138.

### Prime Factorization of 129

Prime factors of 129 are 3, 43. Prime factorization of 129 in exponential form is:

129 = 31 × 431

### Prime Factorization of 138

Prime factors of 138 are 2, 3, 23. Prime factorization of 138 in exponential form is:

138 = 21 × 31 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 129 and 138.

LCM(129,138) = 31 × 431 × 21 × 231
LCM(129,138) = 5934