What is the Least Common Multiple of 19584 and 19596?

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 19584 and 19596 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19584 and 19596, than apply into the LCM equation.

GCF(19584,19596) = 12
LCM(19584,19596) = ( 19584 × 19596) / 12
LCM(19584,19596) = 383768064 / 12
LCM(19584,19596) = 31980672

Least Common Multiple (LCM) of 19584 and 19596 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19584 and 19596. First we will calculate the prime factors of 19584 and 19596.

Prime Factorization of 19584

Prime Factorization of 19596

Now multiplying the highest exponent prime factors to calculate the LCM of 19584 and 19596.

LCM(19584,19596) = 2⁷ × 3² × 17¹ × 23¹ × 71¹
LCM(19584,19596) = 31980672