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What is the Least Common Multiple of 1585 and 1589?

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 1585 and 1589 is 2518565.

LCM(1585,1589) = 2518565

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Least Common Multiple of 1585 and 1589 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1585 and 1589, than apply into the LCM equation.

GCF(1585,1589) = 1
LCM(1585,1589) = ( 1585 × 1589) / 1
LCM(1585,1589) = 2518565 / 1
LCM(1585,1589) = 2518565

Least Common Multiple (LCM) of 1585 and 1589 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1585 and 1589. First we will calculate the prime factors of 1585 and 1589.

Prime Factorization of 1585

Prime factors of 1585 are 5, 317. Prime factorization of 1585 in exponential form is:

1585 = 51 × 3171

Prime Factorization of 1589

Prime factors of 1589 are 7, 227. Prime factorization of 1589 in exponential form is:

1589 = 71 × 2271

Now multiplying the highest exponent prime factors to calculate the LCM of 1585 and 1589.

LCM(1585,1589) = 51 × 3171 × 71 × 2271
LCM(1585,1589) = 2518565