What is the Least Common Multiple of 18105 and 18123?

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 18105 and 18123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18105 and 18123, than apply into the LCM equation.

GCF(18105,18123) = 3
LCM(18105,18123) = ( 18105 × 18123) / 3
LCM(18105,18123) = 328116915 / 3
LCM(18105,18123) = 109372305

Least Common Multiple (LCM) of 18105 and 18123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18105 and 18123. First we will calculate the prime factors of 18105 and 18123.

Prime Factorization of 18105

Prime Factorization of 18123

Now multiplying the highest exponent prime factors to calculate the LCM of 18105 and 18123.

LCM(18105,18123) = 3¹ × 5¹ × 17¹ × 71¹ × 7¹ × 863¹
LCM(18105,18123) = 109372305