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What is the Least Common Multiple of 27045 and 27060?

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 27045 and 27060 is 48789180.

LCM(27045,27060) = 48789180

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Least Common Multiple of 27045 and 27060 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27045 and 27060, than apply into the LCM equation.

GCF(27045,27060) = 15
LCM(27045,27060) = ( 27045 × 27060) / 15
LCM(27045,27060) = 731837700 / 15
LCM(27045,27060) = 48789180

Least Common Multiple (LCM) of 27045 and 27060 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27045 and 27060. First we will calculate the prime factors of 27045 and 27060.

Prime Factorization of 27045

Prime factors of 27045 are 3, 5, 601. Prime factorization of 27045 in exponential form is:

27045 = 32 × 51 × 6011

Prime Factorization of 27060

Prime factors of 27060 are 2, 3, 5, 11, 41. Prime factorization of 27060 in exponential form is:

27060 = 22 × 31 × 51 × 111 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 27045 and 27060.

LCM(27045,27060) = 32 × 51 × 6011 × 22 × 111 × 411
LCM(27045,27060) = 48789180