What is the Least Common Multiple of 1104 and 1116?

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 1104 and 1116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1104 and 1116, than apply into the LCM equation.

GCF(1104,1116) = 12
LCM(1104,1116) = ( 1104 × 1116) / 12
LCM(1104,1116) = 1232064 / 12
LCM(1104,1116) = 102672

Least Common Multiple (LCM) of 1104 and 1116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1104 and 1116. First we will calculate the prime factors of 1104 and 1116.

Prime Factorization of 1104

Prime Factorization of 1116

Now multiplying the highest exponent prime factors to calculate the LCM of 1104 and 1116.

LCM(1104,1116) = 2⁴ × 3² × 23¹ × 31¹
LCM(1104,1116) = 102672