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What is the Least Common Multiple of 27885 and 27900?

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 27885 and 27900 is 51866100.

LCM(27885,27900) = 51866100

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Least Common Multiple of 27885 and 27900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27885 and 27900, than apply into the LCM equation.

GCF(27885,27900) = 15
LCM(27885,27900) = ( 27885 × 27900) / 15
LCM(27885,27900) = 777991500 / 15
LCM(27885,27900) = 51866100

Least Common Multiple (LCM) of 27885 and 27900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27885 and 27900. First we will calculate the prime factors of 27885 and 27900.

Prime Factorization of 27885

Prime factors of 27885 are 3, 5, 11, 13. Prime factorization of 27885 in exponential form is:

27885 = 31 × 51 × 111 × 132

Prime Factorization of 27900

Prime factors of 27900 are 2, 3, 5, 31. Prime factorization of 27900 in exponential form is:

27900 = 22 × 32 × 52 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 27885 and 27900.

LCM(27885,27900) = 32 × 52 × 111 × 132 × 22 × 311
LCM(27885,27900) = 51866100