What is the Least Common Multiple of 1596 and 1608?

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 1608 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 1608, than apply into the LCM equation.

GCF(1596,1608) = 12
LCM(1596,1608) = ( 1596 × 1608) / 12
LCM(1596,1608) = 2566368 / 12
LCM(1596,1608) = 213864

Least Common Multiple (LCM) of 1596 and 1608 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1596 and 1608. First we will calculate the prime factors of 1596 and 1608.

Prime Factorization of 1596

Prime Factorization of 1608

Now multiplying the highest exponent prime factors to calculate the LCM of 1596 and 1608.

LCM(1596,1608) = 2³ × 3¹ × 7¹ × 19¹ × 67¹
LCM(1596,1608) = 213864