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What is the Least Common Multiple of 65585 and 65600?

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 65585 and 65600 is 860475200.

LCM(65585,65600) = 860475200

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Least Common Multiple of 65585 and 65600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65585 and 65600, than apply into the LCM equation.

GCF(65585,65600) = 5
LCM(65585,65600) = ( 65585 × 65600) / 5
LCM(65585,65600) = 4302376000 / 5
LCM(65585,65600) = 860475200

Least Common Multiple (LCM) of 65585 and 65600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65585 and 65600. First we will calculate the prime factors of 65585 and 65600.

Prime Factorization of 65585

Prime factors of 65585 are 5, 13, 1009. Prime factorization of 65585 in exponential form is:

65585 = 51 × 131 × 10091

Prime Factorization of 65600

Prime factors of 65600 are 2, 5, 41. Prime factorization of 65600 in exponential form is:

65600 = 26 × 52 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 65585 and 65600.

LCM(65585,65600) = 52 × 131 × 10091 × 26 × 411
LCM(65585,65600) = 860475200