# What is the Least Common Multiple of 75 and 84?

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 84 is 2100.

LCM(75,84) = 2100

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## Least Common Multiple of 75 and 84 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 84, than apply into the LCM equation.

GCF(75,84) = 3
LCM(75,84) = ( 75 × 84) / 3
LCM(75,84) = 6300 / 3
LCM(75,84) = 2100

## Least Common Multiple (LCM) of 75 and 84 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 84. First we will calculate the prime factors of 75 and 84.

### 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 84

Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:

84 = 22 × 31 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 84.

LCM(75,84) = 31 × 52 × 22 × 71
LCM(75,84) = 2100