What is the Least Common Multiple of 10074 and 10089?

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 10074 and 10089 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10074 and 10089, than apply into the LCM equation.

GCF(10074,10089) = 3
LCM(10074,10089) = ( 10074 × 10089) / 3
LCM(10074,10089) = 101636586 / 3
LCM(10074,10089) = 33878862

Least Common Multiple (LCM) of 10074 and 10089 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10074 and 10089. First we will calculate the prime factors of 10074 and 10089.

Prime Factorization of 10074

Prime Factorization of 10089

Now multiplying the highest exponent prime factors to calculate the LCM of 10074 and 10089.

LCM(10074,10089) = 2¹ × 3² × 23¹ × 73¹ × 19¹ × 59¹
LCM(10074,10089) = 33878862