What is the Least Common Multiple of 1800 and 1819?

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 1819 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 1819, than apply into the LCM equation.

GCF(1800,1819) = 1
LCM(1800,1819) = ( 1800 × 1819) / 1
LCM(1800,1819) = 3274200 / 1
LCM(1800,1819) = 3274200

Least Common Multiple (LCM) of 1800 and 1819 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1819. First we will calculate the prime factors of 1800 and 1819.

Prime Factorization of 1800

Prime Factorization of 1819

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1819.

LCM(1800,1819) = 2³ × 3² × 5² × 17¹ × 107¹
LCM(1800,1819) = 3274200