# What is the Least Common Multiple of 138 and 145?

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 138 and 145 is 20010.

LCM(138,145) = 20010

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## Least Common Multiple of 138 and 145 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 138 and 145, than apply into the LCM equation.

GCF(138,145) = 1
LCM(138,145) = ( 138 × 145) / 1
LCM(138,145) = 20010 / 1
LCM(138,145) = 20010

## Least Common Multiple (LCM) of 138 and 145 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 145. First we will calculate the prime factors of 138 and 145.

### Prime Factorization of 138

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

138 = 21 × 31 × 231

### Prime Factorization of 145

Prime factors of 145 are 5, 29. Prime factorization of 145 in exponential form is:

145 = 51 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 145.

LCM(138,145) = 21 × 31 × 231 × 51 × 291
LCM(138,145) = 20010