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What is the Least Common Multiple of 99585 and 99600?

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 99585 and 99600 is 661244400.

LCM(99585,99600) = 661244400

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Least Common Multiple of 99585 and 99600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 99585 and 99600, than apply into the LCM equation.

GCF(99585,99600) = 15
LCM(99585,99600) = ( 99585 × 99600) / 15
LCM(99585,99600) = 9918666000 / 15
LCM(99585,99600) = 661244400

Least Common Multiple (LCM) of 99585 and 99600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 99585 and 99600. First we will calculate the prime factors of 99585 and 99600.

Prime Factorization of 99585

Prime factors of 99585 are 3, 5, 2213. Prime factorization of 99585 in exponential form is:

99585 = 32 × 51 × 22131

Prime Factorization of 99600

Prime factors of 99600 are 2, 3, 5, 83. Prime factorization of 99600 in exponential form is:

99600 = 24 × 31 × 52 × 831

Now multiplying the highest exponent prime factors to calculate the LCM of 99585 and 99600.

LCM(99585,99600) = 32 × 52 × 22131 × 24 × 831
LCM(99585,99600) = 661244400