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What is the Least Common Multiple of 16566 and 16585?

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 16566 and 16585 is 274747110.

LCM(16566,16585) = 274747110

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Least Common Multiple of 16566 and 16585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16566 and 16585, than apply into the LCM equation.

GCF(16566,16585) = 1
LCM(16566,16585) = ( 16566 × 16585) / 1
LCM(16566,16585) = 274747110 / 1
LCM(16566,16585) = 274747110

Least Common Multiple (LCM) of 16566 and 16585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16566 and 16585. First we will calculate the prime factors of 16566 and 16585.

Prime Factorization of 16566

Prime factors of 16566 are 2, 3, 11, 251. Prime factorization of 16566 in exponential form is:

16566 = 21 × 31 × 111 × 2511

Prime Factorization of 16585

Prime factors of 16585 are 5, 31, 107. Prime factorization of 16585 in exponential form is:

16585 = 51 × 311 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 16566 and 16585.

LCM(16566,16585) = 21 × 31 × 111 × 2511 × 51 × 311 × 1071
LCM(16566,16585) = 274747110