What is the Least Common Multiple of 75288 and 75296?

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 75288 and 75296 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75288 and 75296, than apply into the LCM equation.

GCF(75288,75296) = 8
LCM(75288,75296) = ( 75288 × 75296) / 8
LCM(75288,75296) = 5668885248 / 8
LCM(75288,75296) = 708610656

Least Common Multiple (LCM) of 75288 and 75296 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75288 and 75296. First we will calculate the prime factors of 75288 and 75296.

Prime Factorization of 75288

Prime Factorization of 75296

Now multiplying the highest exponent prime factors to calculate the LCM of 75288 and 75296.

LCM(75288,75296) = 2⁵ × 3¹ × 3137¹ × 13¹ × 181¹
LCM(75288,75296) = 708610656