# What is the Least Common Multiple of 51 and 67?

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 51 and 67 is 3417.

LCM(51,67) = 3417

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## Least Common Multiple of 51 and 67 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51 and 67, than apply into the LCM equation.

GCF(51,67) = 1
LCM(51,67) = ( 51 × 67) / 1
LCM(51,67) = 3417 / 1
LCM(51,67) = 3417

## Least Common Multiple (LCM) of 51 and 67 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51 and 67. First we will calculate the prime factors of 51 and 67.

### Prime Factorization of 51

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

51 = 31 × 171

### Prime Factorization of 67

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 671

Now multiplying the highest exponent prime factors to calculate the LCM of 51 and 67.

LCM(51,67) = 31 × 171 × 671
LCM(51,67) = 3417