What is the Least Common Multiple of 75509 and 75516?

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 75509 and 75516 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75509 and 75516, than apply into the LCM equation.

GCF(75509,75516) = 7
LCM(75509,75516) = ( 75509 × 75516) / 7
LCM(75509,75516) = 5702137644 / 7
LCM(75509,75516) = 814591092

Least Common Multiple (LCM) of 75509 and 75516 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75509 and 75516. First we will calculate the prime factors of 75509 and 75516.

Prime Factorization of 75509

Prime Factorization of 75516

Now multiplying the highest exponent prime factors to calculate the LCM of 75509 and 75516.

LCM(75509,75516) = 7² × 23¹ × 67¹ × 2² × 3¹ × 29¹ × 31¹
LCM(75509,75516) = 814591092