What is the Least Common Multiple of 1074 and 1089?

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 1074 and 1089 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1074 and 1089, than apply into the LCM equation.

GCF(1074,1089) = 3
LCM(1074,1089) = ( 1074 × 1089) / 3
LCM(1074,1089) = 1169586 / 3
LCM(1074,1089) = 389862

Least Common Multiple (LCM) of 1074 and 1089 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1074 and 1089. First we will calculate the prime factors of 1074 and 1089.

Prime Factorization of 1074

Prime Factorization of 1089

Now multiplying the highest exponent prime factors to calculate the LCM of 1074 and 1089.

LCM(1074,1089) = 2¹ × 3² × 179¹ × 11²
LCM(1074,1089) = 389862