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What is the Least Common Multiple of 57045 and 57060?

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 57045 and 57060 is 216999180.

LCM(57045,57060) = 216999180

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Least Common Multiple of 57045 and 57060 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57045 and 57060, than apply into the LCM equation.

GCF(57045,57060) = 15
LCM(57045,57060) = ( 57045 × 57060) / 15
LCM(57045,57060) = 3254987700 / 15
LCM(57045,57060) = 216999180

Least Common Multiple (LCM) of 57045 and 57060 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57045 and 57060. First we will calculate the prime factors of 57045 and 57060.

Prime Factorization of 57045

Prime factors of 57045 are 3, 5, 3803. Prime factorization of 57045 in exponential form is:

57045 = 31 × 51 × 38031

Prime Factorization of 57060

Prime factors of 57060 are 2, 3, 5, 317. Prime factorization of 57060 in exponential form is:

57060 = 22 × 32 × 51 × 3171

Now multiplying the highest exponent prime factors to calculate the LCM of 57045 and 57060.

LCM(57045,57060) = 32 × 51 × 38031 × 22 × 3171
LCM(57045,57060) = 216999180