What is the Least Common Multiple of 1830 and 1845?

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 1830 and 1845 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1830 and 1845, than apply into the LCM equation.

GCF(1830,1845) = 15
LCM(1830,1845) = ( 1830 × 1845) / 15
LCM(1830,1845) = 3376350 / 15
LCM(1830,1845) = 225090

Least Common Multiple (LCM) of 1830 and 1845 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1830 and 1845. First we will calculate the prime factors of 1830 and 1845.

Prime Factorization of 1830

Prime Factorization of 1845

Now multiplying the highest exponent prime factors to calculate the LCM of 1830 and 1845.

LCM(1830,1845) = 2¹ × 3² × 5¹ × 61¹ × 41¹
LCM(1830,1845) = 225090