What is the Least Common Multiple of 1584 and 1596?

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 1584 and 1596 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1584 and 1596, than apply into the LCM equation.

GCF(1584,1596) = 12
LCM(1584,1596) = ( 1584 × 1596) / 12
LCM(1584,1596) = 2528064 / 12
LCM(1584,1596) = 210672

Least Common Multiple (LCM) of 1584 and 1596 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1584 and 1596. First we will calculate the prime factors of 1584 and 1596.

Prime Factorization of 1584

Prime Factorization of 1596

Now multiplying the highest exponent prime factors to calculate the LCM of 1584 and 1596.

LCM(1584,1596) = 2⁴ × 3² × 11¹ × 7¹ × 19¹
LCM(1584,1596) = 210672