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What is the Least Common Multiple of 10586 and 10604?

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 10586 and 10604 is 56126972.

LCM(10586,10604) = 56126972

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Least Common Multiple of 10586 and 10604 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10586 and 10604, than apply into the LCM equation.

GCF(10586,10604) = 2
LCM(10586,10604) = ( 10586 × 10604) / 2
LCM(10586,10604) = 112253944 / 2
LCM(10586,10604) = 56126972

Least Common Multiple (LCM) of 10586 and 10604 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10586 and 10604. First we will calculate the prime factors of 10586 and 10604.

Prime Factorization of 10586

Prime factors of 10586 are 2, 67, 79. Prime factorization of 10586 in exponential form is:

10586 = 21 × 671 × 791

Prime Factorization of 10604

Prime factors of 10604 are 2, 11, 241. Prime factorization of 10604 in exponential form is:

10604 = 22 × 111 × 2411

Now multiplying the highest exponent prime factors to calculate the LCM of 10586 and 10604.

LCM(10586,10604) = 22 × 671 × 791 × 111 × 2411
LCM(10586,10604) = 56126972