What is the Least Common Multiple of 1608 and 1623?

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 1608 and 1623 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1608 and 1623, than apply into the LCM equation.

GCF(1608,1623) = 3
LCM(1608,1623) = ( 1608 × 1623) / 3
LCM(1608,1623) = 2609784 / 3
LCM(1608,1623) = 869928

Least Common Multiple (LCM) of 1608 and 1623 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1608 and 1623. First we will calculate the prime factors of 1608 and 1623.

Prime Factorization of 1608

Prime Factorization of 1623

Now multiplying the highest exponent prime factors to calculate the LCM of 1608 and 1623.

LCM(1608,1623) = 2³ × 3¹ × 67¹ × 541¹
LCM(1608,1623) = 869928