# What is the Least Common Multiple of 34 and 51?

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 34 and 51 is 102.

LCM(34,51) = 102

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## Least Common Multiple of 34 and 51 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 51, than apply into the LCM equation.

GCF(34,51) = 17
LCM(34,51) = ( 34 × 51) / 17
LCM(34,51) = 1734 / 17
LCM(34,51) = 102

## Least Common Multiple (LCM) of 34 and 51 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 51. First we will calculate the prime factors of 34 and 51.

### Prime Factorization of 34

Prime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:

34 = 21 × 171

### Prime Factorization of 51

Prime factors of 51 are 3, 17. Prime factorization of 51 in exponential form is:

51 = 31 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 51.

LCM(34,51) = 21 × 171 × 31
LCM(34,51) = 102