# What is the Least Common Multiple of 138 and 146?

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 146 is 10074.

LCM(138,146) = 10074

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## Least Common Multiple of 138 and 146 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 146, than apply into the LCM equation.

GCF(138,146) = 2
LCM(138,146) = ( 138 × 146) / 2
LCM(138,146) = 20148 / 2
LCM(138,146) = 10074

## Least Common Multiple (LCM) of 138 and 146 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 146. First we will calculate the prime factors of 138 and 146.

### 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 146

Prime factors of 146 are 2, 73. Prime factorization of 146 in exponential form is:

146 = 21 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 146.

LCM(138,146) = 21 × 31 × 231 × 731
LCM(138,146) = 10074