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What is the Least Common Multiple of 30192 and 30205?

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 30192 and 30205 is 911949360.

LCM(30192,30205) = 911949360

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Least Common Multiple of 30192 and 30205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30192 and 30205, than apply into the LCM equation.

GCF(30192,30205) = 1
LCM(30192,30205) = ( 30192 × 30205) / 1
LCM(30192,30205) = 911949360 / 1
LCM(30192,30205) = 911949360

Least Common Multiple (LCM) of 30192 and 30205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30192 and 30205. First we will calculate the prime factors of 30192 and 30205.

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

Prime Factorization of 30205

Prime factors of 30205 are 5, 7, 863. Prime factorization of 30205 in exponential form is:

30205 = 51 × 71 × 8631

Now multiplying the highest exponent prime factors to calculate the LCM of 30192 and 30205.

LCM(30192,30205) = 24 × 31 × 171 × 371 × 51 × 71 × 8631
LCM(30192,30205) = 911949360