What is the Least Common Multiple of 1854 and 1860?

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 1854 and 1860 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1854 and 1860, than apply into the LCM equation.

GCF(1854,1860) = 6
LCM(1854,1860) = ( 1854 × 1860) / 6
LCM(1854,1860) = 3448440 / 6
LCM(1854,1860) = 574740

Least Common Multiple (LCM) of 1854 and 1860 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1854 and 1860. First we will calculate the prime factors of 1854 and 1860.

Prime Factorization of 1854

Prime Factorization of 1860

Now multiplying the highest exponent prime factors to calculate the LCM of 1854 and 1860.

LCM(1854,1860) = 2² × 3² × 103¹ × 5¹ × 31¹
LCM(1854,1860) = 574740