What is the Least Common Multiple of 1800 and 1808?

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 1808 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 1808, than apply into the LCM equation.

GCF(1800,1808) = 8
LCM(1800,1808) = ( 1800 × 1808) / 8
LCM(1800,1808) = 3254400 / 8
LCM(1800,1808) = 406800

Least Common Multiple (LCM) of 1800 and 1808 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1808. First we will calculate the prime factors of 1800 and 1808.

Prime Factorization of 1800

Prime Factorization of 1808

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1808.

LCM(1800,1808) = 2⁴ × 3² × 5² × 113¹
LCM(1800,1808) = 406800