What is the Least Common Multiple of 10584 and 10600?

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 10584 and 10600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10584 and 10600, than apply into the LCM equation.

GCF(10584,10600) = 8
LCM(10584,10600) = ( 10584 × 10600) / 8
LCM(10584,10600) = 112190400 / 8
LCM(10584,10600) = 14023800

Least Common Multiple (LCM) of 10584 and 10600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10584 and 10600. First we will calculate the prime factors of 10584 and 10600.

Prime Factorization of 10584

Prime Factorization of 10600

Now multiplying the highest exponent prime factors to calculate the LCM of 10584 and 10600.

LCM(10584,10600) = 2³ × 3³ × 7² × 5² × 53¹
LCM(10584,10600) = 14023800