What is the Least Common Multiple of 75306 and 75321?

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 75306 and 75321 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75306 and 75321, than apply into the LCM equation.

GCF(75306,75321) = 3
LCM(75306,75321) = ( 75306 × 75321) / 3
LCM(75306,75321) = 5672123226 / 3
LCM(75306,75321) = 1890707742

Least Common Multiple (LCM) of 75306 and 75321 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75306 and 75321. First we will calculate the prime factors of 75306 and 75321.

Prime Factorization of 75306

Prime Factorization of 75321

Now multiplying the highest exponent prime factors to calculate the LCM of 75306 and 75321.

LCM(75306,75321) = 2¹ × 3² × 7¹ × 11¹ × 163¹ × 8369¹
LCM(75306,75321) = 1890707742