# What is the Least Common Multiple of 165 and 174?

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 165 and 174 is 9570.

LCM(165,174) = 9570

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## Least Common Multiple of 165 and 174 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 165 and 174, than apply into the LCM equation.

GCF(165,174) = 3
LCM(165,174) = ( 165 × 174) / 3
LCM(165,174) = 28710 / 3
LCM(165,174) = 9570

## Least Common Multiple (LCM) of 165 and 174 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 165 and 174. First we will calculate the prime factors of 165 and 174.

### Prime Factorization of 165

Prime factors of 165 are 3, 5, 11. Prime factorization of 165 in exponential form is:

165 = 31 × 51 × 111

### Prime Factorization of 174

Prime factors of 174 are 2, 3, 29. Prime factorization of 174 in exponential form is:

174 = 21 × 31 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 165 and 174.

LCM(165,174) = 31 × 51 × 111 × 21 × 291
LCM(165,174) = 9570