What is the Least Common Multiple of 1608 and 1628?

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 1628 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 1628, than apply into the LCM equation.

GCF(1608,1628) = 4
LCM(1608,1628) = ( 1608 × 1628) / 4
LCM(1608,1628) = 2617824 / 4
LCM(1608,1628) = 654456

Least Common Multiple (LCM) of 1608 and 1628 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1608 and 1628. First we will calculate the prime factors of 1608 and 1628.

Prime Factorization of 1608

Prime Factorization of 1628

Now multiplying the highest exponent prime factors to calculate the LCM of 1608 and 1628.

LCM(1608,1628) = 2³ × 3¹ × 67¹ × 11¹ × 37¹
LCM(1608,1628) = 654456