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What is the Least Common Multiple of 30192 and 30204?

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 30204 is 75993264.

LCM(30192,30204) = 75993264

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Least Common Multiple of 30192 and 30204 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 30204, than apply into the LCM equation.

GCF(30192,30204) = 12
LCM(30192,30204) = ( 30192 × 30204) / 12
LCM(30192,30204) = 911919168 / 12
LCM(30192,30204) = 75993264

Least Common Multiple (LCM) of 30192 and 30204 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30192 and 30204. First we will calculate the prime factors of 30192 and 30204.

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 30204

Prime factors of 30204 are 2, 3, 839. Prime factorization of 30204 in exponential form is:

30204 = 22 × 32 × 8391

Now multiplying the highest exponent prime factors to calculate the LCM of 30192 and 30204.

LCM(30192,30204) = 24 × 32 × 171 × 371 × 8391
LCM(30192,30204) = 75993264