What is the Least Common Multiple of 75309 and 75313?

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 75309 and 75313 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75309 and 75313, than apply into the LCM equation.

GCF(75309,75313) = 1
LCM(75309,75313) = ( 75309 × 75313) / 1
LCM(75309,75313) = 5671746717 / 1
LCM(75309,75313) = 5671746717

Least Common Multiple (LCM) of 75309 and 75313 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75309 and 75313. First we will calculate the prime factors of 75309 and 75313.

Prime Factorization of 75309

Prime Factorization of 75313

Now multiplying the highest exponent prime factors to calculate the LCM of 75309 and 75313.

LCM(75309,75313) = 3¹ × 13¹ × 1931¹ × 7² × 29¹ × 53¹
LCM(75309,75313) = 5671746717