What is the Least Common Multiple of 1089 and 1104?

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 1089 and 1104 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1089 and 1104, than apply into the LCM equation.

GCF(1089,1104) = 3
LCM(1089,1104) = ( 1089 × 1104) / 3
LCM(1089,1104) = 1202256 / 3
LCM(1089,1104) = 400752

Least Common Multiple (LCM) of 1089 and 1104 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1089 and 1104. First we will calculate the prime factors of 1089 and 1104.

Prime Factorization of 1089

Prime Factorization of 1104

Now multiplying the highest exponent prime factors to calculate the LCM of 1089 and 1104.

LCM(1089,1104) = 3² × 11² × 2⁴ × 23¹
LCM(1089,1104) = 400752