What is the Least Common Multiple of 9105 and 9114?

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 9105 and 9114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9105 and 9114, than apply into the LCM equation.

GCF(9105,9114) = 3
LCM(9105,9114) = ( 9105 × 9114) / 3
LCM(9105,9114) = 82982970 / 3
LCM(9105,9114) = 27660990

Least Common Multiple (LCM) of 9105 and 9114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9105 and 9114. First we will calculate the prime factors of 9105 and 9114.

Prime Factorization of 9105

Prime Factorization of 9114

Now multiplying the highest exponent prime factors to calculate the LCM of 9105 and 9114.

LCM(9105,9114) = 3¹ × 5¹ × 607¹ × 2¹ × 7² × 31¹
LCM(9105,9114) = 27660990