What is the Least Common Multiple of 75294 and 75309?

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 75294 and 75309 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75294 and 75309, than apply into the LCM equation.

GCF(75294,75309) = 3
LCM(75294,75309) = ( 75294 × 75309) / 3
LCM(75294,75309) = 5670315846 / 3
LCM(75294,75309) = 1890105282

Least Common Multiple (LCM) of 75294 and 75309 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75294 and 75309. First we will calculate the prime factors of 75294 and 75309.

Prime Factorization of 75294

Prime Factorization of 75309

Now multiplying the highest exponent prime factors to calculate the LCM of 75294 and 75309.

LCM(75294,75309) = 2¹ × 3² × 47¹ × 89¹ × 13¹ × 1931¹
LCM(75294,75309) = 1890105282