What is the Least Common Multiple of 1596 and 1609?

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 1596 and 1609 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1596 and 1609, than apply into the LCM equation.

GCF(1596,1609) = 1
LCM(1596,1609) = ( 1596 × 1609) / 1
LCM(1596,1609) = 2567964 / 1
LCM(1596,1609) = 2567964

Least Common Multiple (LCM) of 1596 and 1609 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1596 and 1609. First we will calculate the prime factors of 1596 and 1609.

Prime Factorization of 1596

Prime Factorization of 1609

Now multiplying the highest exponent prime factors to calculate the LCM of 1596 and 1609.

LCM(1596,1609) = 2² × 3¹ × 7¹ × 19¹ × 1609¹
LCM(1596,1609) = 2567964