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What is the Least Common Multiple of 30081 and 30096?

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 30081 and 30096 is 301772592.

LCM(30081,30096) = 301772592

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Least Common Multiple of 30081 and 30096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30081 and 30096, than apply into the LCM equation.

GCF(30081,30096) = 3
LCM(30081,30096) = ( 30081 × 30096) / 3
LCM(30081,30096) = 905317776 / 3
LCM(30081,30096) = 301772592

Least Common Multiple (LCM) of 30081 and 30096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30081 and 30096. First we will calculate the prime factors of 30081 and 30096.

Prime Factorization of 30081

Prime factors of 30081 are 3, 37, 271. Prime factorization of 30081 in exponential form is:

30081 = 31 × 371 × 2711

Prime Factorization of 30096

Prime factors of 30096 are 2, 3, 11, 19. Prime factorization of 30096 in exponential form is:

30096 = 24 × 32 × 111 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 30081 and 30096.

LCM(30081,30096) = 32 × 371 × 2711 × 24 × 111 × 191
LCM(30081,30096) = 301772592