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What is the Least Common Multiple of 75307 and 75312?

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 75307 and 75312 is 5671520784.

LCM(75307,75312) = 5671520784

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Least Common Multiple of 75307 and 75312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75307 and 75312, than apply into the LCM equation.

GCF(75307,75312) = 1
LCM(75307,75312) = ( 75307 × 75312) / 1
LCM(75307,75312) = 5671520784 / 1
LCM(75307,75312) = 5671520784

Least Common Multiple (LCM) of 75307 and 75312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75307 and 75312. First we will calculate the prime factors of 75307 and 75312.

Prime Factorization of 75307

Prime factors of 75307 are 75307. Prime factorization of 75307 in exponential form is:

75307 = 753071

Prime Factorization of 75312

Prime factors of 75312 are 2, 3, 523. Prime factorization of 75312 in exponential form is:

75312 = 24 × 32 × 5231

Now multiplying the highest exponent prime factors to calculate the LCM of 75307 and 75312.

LCM(75307,75312) = 753071 × 24 × 32 × 5231
LCM(75307,75312) = 5671520784