What is the Least Common Multiple of 1110 and 1125?

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 1110 and 1125 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1110 and 1125, than apply into the LCM equation.

GCF(1110,1125) = 15
LCM(1110,1125) = ( 1110 × 1125) / 15
LCM(1110,1125) = 1248750 / 15
LCM(1110,1125) = 83250

Least Common Multiple (LCM) of 1110 and 1125 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1110 and 1125. First we will calculate the prime factors of 1110 and 1125.

Prime Factorization of 1110

Prime Factorization of 1125

Now multiplying the highest exponent prime factors to calculate the LCM of 1110 and 1125.

LCM(1110,1125) = 2¹ × 3² × 5³ × 37¹
LCM(1110,1125) = 83250