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What is the Least Common Multiple of 30175 and 30192?

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 30175 and 30192 is 53590800.

LCM(30175,30192) = 53590800

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Least Common Multiple of 30175 and 30192 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30175 and 30192, than apply into the LCM equation.

GCF(30175,30192) = 17
LCM(30175,30192) = ( 30175 × 30192) / 17
LCM(30175,30192) = 911043600 / 17
LCM(30175,30192) = 53590800

Least Common Multiple (LCM) of 30175 and 30192 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30175 and 30192. First we will calculate the prime factors of 30175 and 30192.

Prime Factorization of 30175

Prime factors of 30175 are 5, 17, 71. Prime factorization of 30175 in exponential form is:

30175 = 52 × 171 × 711

Prime Factorization of 30192

Prime factors of 30192 are 2, 3, 17, 37. Prime factorization of 30192 in exponential form is:

30192 = 24 × 31 × 171 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 30175 and 30192.

LCM(30175,30192) = 52 × 171 × 711 × 24 × 31 × 371
LCM(30175,30192) = 53590800