What is the Least Common Multiple of 75296 and 75300?

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 75296 and 75300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75296 and 75300, than apply into the LCM equation.

GCF(75296,75300) = 4
LCM(75296,75300) = ( 75296 × 75300) / 4
LCM(75296,75300) = 5669788800 / 4
LCM(75296,75300) = 1417447200

Least Common Multiple (LCM) of 75296 and 75300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75296 and 75300. First we will calculate the prime factors of 75296 and 75300.

Prime Factorization of 75296

Prime Factorization of 75300

Now multiplying the highest exponent prime factors to calculate the LCM of 75296 and 75300.

LCM(75296,75300) = 2⁵ × 13¹ × 181¹ × 3¹ × 5² × 251¹
LCM(75296,75300) = 1417447200