What is the Least Common Multiple of 10578 and 10584?

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 of 10578 and 10584 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 10584, than apply into the LCM equation.

GCF(10578,10584) = 6
LCM(10578,10584) = ( 10578 × 10584) / 6
LCM(10578,10584) = 111957552 / 6
LCM(10578,10584) = 18659592

Least Common Multiple (LCM) of 10578 and 10584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10578 and 10584. First we will calculate the prime factors of 10578 and 10584.

Prime Factorization of 10578

Prime Factorization of 10584

Now multiplying the highest exponent prime factors to calculate the LCM of 10578 and 10584.

LCM(10578,10584) = 2³ × 3³ × 41¹ × 43¹ × 7²
LCM(10578,10584) = 18659592