# What is the Least Common Multiple of 75 and 86?

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 75 and 86 is 6450.

LCM(75,86) = 6450

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## Least Common Multiple of 75 and 86 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75 and 86, than apply into the LCM equation.

GCF(75,86) = 1
LCM(75,86) = ( 75 × 86) / 1
LCM(75,86) = 6450 / 1
LCM(75,86) = 6450

## Least Common Multiple (LCM) of 75 and 86 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 86. First we will calculate the prime factors of 75 and 86.

### Prime Factorization of 75

Prime factors of 75 are 3, 5. Prime factorization of 75 in exponential form is:

75 = 31 × 52

### Prime Factorization of 86

Prime factors of 86 are 2, 43. Prime factorization of 86 in exponential form is:

86 = 21 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 86.

LCM(75,86) = 31 × 52 × 21 × 431
LCM(75,86) = 6450