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What is the Least Common Multiple of 10578 and 10583?

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 10578 and 10583 is 111946974.

LCM(10578,10583) = 111946974

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Least Common Multiple of 10578 and 10583 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10578 and 10583, than apply into the LCM equation.

GCF(10578,10583) = 1
LCM(10578,10583) = ( 10578 × 10583) / 1
LCM(10578,10583) = 111946974 / 1
LCM(10578,10583) = 111946974

Least Common Multiple (LCM) of 10578 and 10583 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10578 and 10583. First we will calculate the prime factors of 10578 and 10583.

Prime Factorization of 10578

Prime factors of 10578 are 2, 3, 41, 43. Prime factorization of 10578 in exponential form is:

10578 = 21 × 31 × 411 × 431

Prime Factorization of 10583

Prime factors of 10583 are 19, 557. Prime factorization of 10583 in exponential form is:

10583 = 191 × 5571

Now multiplying the highest exponent prime factors to calculate the LCM of 10578 and 10583.

LCM(10578,10583) = 21 × 31 × 411 × 431 × 191 × 5571
LCM(10578,10583) = 111946974