What is the Least Common Multiple of 1800 and 1805?

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 1800 and 1805 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1800 and 1805, than apply into the LCM equation.

GCF(1800,1805) = 5
LCM(1800,1805) = ( 1800 × 1805) / 5
LCM(1800,1805) = 3249000 / 5
LCM(1800,1805) = 649800

Least Common Multiple (LCM) of 1800 and 1805 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1805. First we will calculate the prime factors of 1800 and 1805.

Prime Factorization of 1800

Prime Factorization of 1805

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1805.

LCM(1800,1805) = 2³ × 3² × 5² × 19²
LCM(1800,1805) = 649800