# What is the Least Common Multiple of 75 and 88?

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 88 is 6600.

LCM(75,88) = 6600

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## Least Common Multiple of 75 and 88 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 88, than apply into the LCM equation.

GCF(75,88) = 1
LCM(75,88) = ( 75 × 88) / 1
LCM(75,88) = 6600 / 1
LCM(75,88) = 6600

## Least Common Multiple (LCM) of 75 and 88 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 88. First we will calculate the prime factors of 75 and 88.

### 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 88

Prime factors of 88 are 2, 11. Prime factorization of 88 in exponential form is:

88 = 23 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 88.

LCM(75,88) = 31 × 52 × 23 × 111
LCM(75,88) = 6600